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Cowgirl boots for women usually made from high quality leather. Usually have a brown color, but now, there are also provided many kinds of color such as red, pink, green, blue, etc. They feature of cowgirl boots is the unique and ethnic ornament, the model, and of course the sole and the heel. They seems to be gorgeous if worn by women matching combined with flannel shirt, jeans, cowgirl hat, and brown leather belt. It would look so cool and has a character. I always dreaming that could wear those cowgirl outfits by riding a horse. Sounds perfect!
This cowgirl boots for women become popular after the country music and cowboy movie have been popular. There is no need to be a true cowboy or born in the old west to wear and look good with cowgirl boots for women. While the cowgirl boots might be expensive, it would last you for a long time. And make sure to wear a neutral color cowgirl boots for women in order to could be worn often and matching with many kinds of outfits. If you want to some modern style, you could try to wear skinny jeans then top it of with a dress and wear you cowgirl boots.
Tags: cowgirl boots for women.


text:
William Porter
National | mycolumbuspower Staff
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Arguing that it would delay the upcoming trials of three other officers, Baltimore judge Barry Williams on Wednesday ruled that prosecutors cannot compel William Porter to testify at their trials, according to The Associated Press. Porter's testimony was the cornerstone of Baltimore State's Attorney Marilyn Mosby's case against five other officers charged in the death of 25-year-old […]
Freddie Gray Case: William Porter Ordered To Testify Against Second Cop
Jury selection in Baltimore police officer Caesar Goodson's trial is set to begin on Monday in the Freddie Gray case.
Closing statements were heard Monday, leading the jury into deliberations to determine the fate of William Porter, one of six Baltimore officers charged in the death of Freddie Gray.
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redpajama_set_name: RedPajamaCommonCrawl


The late, great Aretha Franklin has been posthumously awarded the Pulitzer Prize.
Since 1918, a total of 44 "Special Citation" awards have been given out. Bob Dylan, Hank Williams, John Coltrane, and Duke Ellington are among the past music recipients.
Franklin died less than a year ago, in August 2018, due to advance pancreatic cancer of the neuroendrocrine type. She was only 76 years old.
Last year, Kendrick Lamar scored the Pulitzer Prize in Music for DAMN., marking the first time a non-classic or jazz artist won in the category.
To own all of Franklin's releases on vinyl, head here.


text:
8: Measurable Functions and Integration
Book: Introduction to Real Analysis (Lebl)
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8.3: Measurable Functions in \((S, \mathcal{M}, m)\)
Junalyn
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Username: junalyn2020
Elias Zakon
University of Windsor via The Trilla Group (support by Saylor Foundation)
Corollary \(\PageIndex{1}\)
Lemma \(\PageIndex{1}\)
Theorem \(\PageIndex{1}\)
*Theorem \(\PageIndex{2}\)
*Lemma \(\PageIndex{3}\)
I. Henceforth we shall presuppose not just a measurable space (§1) but a measure space \((S, \mathcal{M}, m),\) where \(m : \mathcal{M} \rightarrow E^{*}\) is a measure on a \(\sigma\) -ring \(\mathcal{M} \subseteq 2^{S}\).
We saw in Chapter 7 that one could often neglect sets of Lebesgue measure zero on \(E^{n}-\) if a property held everywhere except on a set of Lebesgue measure zero, we said it held "almost everywhere." The following definition generalizes this usage.
We say that a property \(P(x)\) holds for almost all \(x \in A\) (with respect to the measure \(m )\) or almost everywhere (a.e. \((m) )\) on \(A\) iff it holds on \(A-Q\) for some \(Q \in \mathcal{M}\) with \(m Q=0\).
Thus we write
f_{n} \rightarrow f(a . e .) \text { or } f=\lim f_{n}(a . e .(m)) \text { on } A
iff \(f_{n} \rightarrow f(\text { pointwise })\) on \(A-Q, m Q=0 .\) Of course, "pointwise" implies \(" a . e . "(\text { take } Q=\emptyset),\) but the converse fails.
We say that \(f : S \rightarrow\left(T, \rho^{\prime}\right)\) is almost measurable on \(A\) iff \(A \in \mathcal{M}\) and \(f\) is \(\mathcal{M}\) -measurable on \(A-Q, m Q=0\).
We then also say that \(f\) is \(m\) -measurable (\(m\) being the measure involved ) as opposed to \(\mathcal{M}\)-measurable.
Observe that we may assume \(Q \subseteq A\) here (replace \(Q\) by \(A \cap Q )\).
*Note 1. If \(m\) is a generalized measure (Chapter 7, §11), replace \(m Q=0\) by \(v_{m} Q=0\left(v_{m}=\text { total variation of } m\right)\) in Definitions 1 and 2 and in the following proofs.
If the functions
f_{n} : S \rightarrow\left(T, \rho^{\prime}\right), \quad n=1,2, \ldots
are \(m\)-measurable on \(A,\) and if
f_{n} \rightarrow f(a . e .(m))
on \(A,\) then \(f\) is \(m\)-measurable on \(A\).
By assumption, \(f_{n} \rightarrow f (\text { pointwise })\) on \(A-Q_{0}, m Q_{0}=0 .\) Also, \(f_{n}\) is \(\mathcal{M}\)-measurable on
A-Q_{n}, m Q_{n}=0, \quad n=1,2, \dots
(The \(Q_{n}\) need not be the same.)
Q=\bigcup_{n=0}^{\infty} Q_{n};
m Q \leq \sum_{n=0}^{\infty} m Q_{n}=0.
By Corollary 2 in §1, all \(f_{n}\) are \(\mathcal{M}\)-measurable on \(A-Q\) (why?), and \(f_{n} \rightarrow f\)
(pointwise) on \(A-Q,\) as \(A-Q \subseteq A-Q_{0} .\)
Thus by Theorem 4 in §1, \(f\) is \(\mathcal{M}\) -measurable on \(A-Q .\) As \(m Q=0\), this
is the desired result. \(\square\)
If \(f=g (a . e .(m))\) on \(A\) and \(f\) is \(m\)-measurable on \(A,\) so is \(g\).
By assumption, \(f=g\) on \(A-Q_{1}\) and \(f\) is \(\mathcal{M}\)-measurable on \(A-Q_{2}\), with \(m Q_{1}=m Q_{2}=0\).
Let \(Q=Q_{1} \cup Q_{2} .\) Then \(m Q=0\) and \(g=f\) on \(A-Q .\) (Why? \()\)
By Corollary 2 of §1, \(f\) is \(\mathcal{M}\)-measurable on \(A-Q\). Hence so is \(g\), as claimed. \(\square\)
If \(f : S \rightarrow\left(T, \rho^{\prime}\right)\) is \(m\) -measurable on \(A,\) then
f=\lim _{n \rightarrow \infty} f_{n} (\text {uniformly}) \text { on } A-Q(m Q=0),
for some maps \(f_{n},\) all elementary on \(A-Q\).
Add proof here and it will automatically be hidden
(Compare Corollary 3 with Theorem 3 in §1).
Quite similarly all other propositions of §1 carry over to almost measurable (i.e., \(m\) -measurable) functions. Note, however, that the term "measurable" in §§1 and 2 always meant \(" \mathcal{M}\) -measurable." This implies \(m\)-measurability (take \(Q=\emptyset ),\) but the converse fails. (See Note \(2,\) however.)
We still obtain the following result.
f_{n} : S \rightarrow E^{*} \quad(n=1,2, \ldots)
are \(m\)-measurable on a set \(A,\) so also are
\sup f_{n}, \inf f_{n}, \overline{\lim } f_{n}, \text { and } \underline{\lim} f_{n}
(Use Lemma 1 of §2).
Similarly, Theorem 2 in §2 carries over to \(m\)-measurable functions.
Note 2. If \(m\) is complete (such as Lebesgue measure and LS measures) then, for \(f : S \rightarrow E^{*}\left(E^{n}, C^{n}\right), m-\) and \(\mathcal{M}\)-measurability coincide (see Problem 3 below).
II. Measurability and Continuity. To study the connection between these notions, we first state two lemmas, often treated as definitions.
\(A \operatorname{map} f : S \rightarrow E^{n}\left(C^{n}\right)\) is \(\mathcal{M}\)-measurable on \(A\) iff
A \cap f^{-1}[B] \in \mathcal{M}
for each Borel set (equivalently, open set) \(B\) in \(E^{n}\left(C^{n}\right)\).
See Problems \(8-10\) in §2 for a sketch of the proof.
\(A \operatorname{map} f :(S, \rho) \rightarrow\left(T, \rho^{\prime}\right)\) is relatively continuous on \(A \subseteq S\) iff for any open set \(B \subseteq\left(T, \rho^{\prime}\right),\) the set \(A \cap f^{-1}[B]\) is open in \((A, \rho)\) as a subspace of \((S, \rho)\).
(This holds also with "open" replaced by "closed.")
By Chapter 4, §1, footnote \(4, f\) is relatively continuous on \(A\) iff its restriction to \(A\) (call it \(g : A \rightarrow T )\) is continuous in the ordinary sense.
Now, by Problem 15\((\mathrm{iv})(\mathrm{v})\) in Chapter 4, §2, with \(S\) replaced by \(A,\) this means that \(g^{-1}[B]\) is open (closed) \(i n(A, \rho)\) when \(B\) is so in \(\left(T, \rho^{\prime}\right) .\) But
g^{-1}[B]=\{x \in A | f(x) \in B\}=A \cap f^{-1}[B].
(Why?) Hence the result follows. \(\square\)
Let \(m : \mathcal{M} \rightarrow E^{*}\) be a topological measure in \((S, \rho) .\) If \(f : S \rightarrow\) \(E^{n}\left(C^{n}\right)\) is relatively continuous on a set \(A \in \mathcal{M},\) it is \(\mathcal{M}\) -measurable on \(A\).
Let \(B\) be open in \(E^{n}\left(C^{n}\right) .\) By Lemma 2,
A \cap f^{-1}[B]
is open \(i n(A, \rho) .\) Hence by Theorem 4 of Chapter 3, §12,
A \cap f^{-1}[B]=A \cap U
for some open set \(U\) in \((S, \rho)\).
Now, by assumption, \(A\) is in \(\mathcal{M} .\) So is \(U,\) as \(\mathcal{M}\) is topological \((\mathcal{M} \supseteq \mathcal{G})\).
A \cap f^{-1}[B]=A \cap U \in \mathcal{M}
for any open \(B \subseteq E^{n}\left(C^{n}\right) .\) The result follows by Lemma 1. \(\square\)
Note 3. The converse fails. For example, the Dirichlet function (Example \((\mathrm{c})\) in Chapter 4, §1) is L-measurable (even simple) but discontinuous everywhere.
Note 4. Lemma 1 and Theorem 1 hold for a map \(f : S \rightarrow\left(T, \rho^{\prime}\right),\) too, provided \(f[A]\) is separable, i.e.,
f[A] \subseteq \overline{D}
for a countable set \(D \subseteq T\) (cf. Problem 11 in §2).
*III. For strongly regular measures (Definition 5 in Chapter 7, §7), we obtain the following theorem.
(Luzin). Let \(m : \mathcal{M} \rightarrow E^{*}\) be a strongly regular measure in \((S, \rho)\). Let \(f : S \rightarrow\left(T, \rho^{\prime}\right)\) be \(m\)-measurable on \(A\).
Then given \(\varepsilon>0,\) there is a closed set \(F \subseteq A(F \in \mathcal{M})\) such that
m(A-F)<\varepsilon
and \(f\) is relatively continuous on \(F\).
(Note that if \(T=E^{*}, \rho^{\prime}\) is as in Problem 5 of Chapter 3, §11.)
By assumption, \(f\) is \(\mathcal{M}\)-measurable on a set
H=A-Q, m Q=0;
so by Problem 7 in §1, \(f[H]\) is separable in \(T\). We may safely assume that \(f\) is \(\mathcal{M}\)-measurable on \(S\) and that all of \(T\) is separable. (If not, replace \(S\) and \(T\) by \(H\) and \(f[H],\) restricting \(f\) to \(H,\) and \(m\) to \(\mathcal{M}\)-sets inside \(H ;\) see also Problems 7 and 8 below.)
Then by Problem 12 of §2, we can fix globes \(G_{1}, G_{2}, \ldots\) in \(T\) such that
\text { each open set } B \neq \emptyset \text { in } T \text { is the union of a subsequence of }\left\{G_{k}\right\}.
Now let \(\varepsilon>0,\) and set
S_{k}=S \cap f^{-1}\left[G_{k}\right]=f^{-1}\left[G_{k}\right], \quad k=1,2, \ldots
By Corollary 2 in §2, \(S_{k} \in \mathcal{M} .\) As \(m\) is strongly regular, we find for each \(S_{k}\) an open set
U_{k} \supseteq S_{k},
with \(U_{k} \in \mathcal{M}\) and
m\left(U_{k}-S_{k}\right)<\frac{\varepsilon}{2^{k+1}}.
Let \(B_{k}=U_{k}-S_{k}, D=\bigcup_{k} B_{k} ;\) so \(D \in \mathcal{M}\) and
m D \leq \sum_{k} m B_{k} \leq \sum_{k} \frac{\varepsilon}{2^{k+1}} \leq \frac{1}{2} \varepsilon
U_{k}-B_{k}=S_{k}=f^{-1}\left[G_{k}\right].
As \(D=\bigcup B_{k},\) we have
(\forall k) \quad B_{k}-D=B_{k} \cap(-D)=\emptyset.
Hence by \(\left(2^{\prime}\right)\),
\begin{aligned}(\forall k) \quad f^{-1}\left[G_{k}\right] \cap(-D) &=\left(U_{k}-B_{k}\right) \cap(-D) \\ &=\left(U_{k} \cap(-D)\right)-\left(B_{k} \cap(-D)\right)=U_{k} \cap(-D) \end{aligned}.
Combining this with \((1),\) we have, for each open set \(B=\bigcup_{i} G_{k_{i}} \operatorname{in} T\),
f^{-1}[B] \cap(-D)=\bigcup_{i} f^{-1}\left[G_{k_{i}}\right] \cap(-D)=\bigcup_{i} U_{k_{i}} \cap(-D).
since the \(U_{k_{i}}\) are open in \(S\) (by construction), the set \((3)\) is open in \(S-D\) as a subspace of \(S .\) By Lemma \(2,\) then, \(f\) is relatively continuous on \(S-D,\) or rather on
H-D=A-Q-D
(since we actually substituted \(S\) for \(H\) in the course of the proof). As \(m Q=0\) and \(m D<\frac{1}{2} \varepsilon\) by \((2)\),
m(H-D)<m A-\frac{1}{2} \varepsilon.
Finally, as \(m\) is strongly regular and \(H-D \in \mathcal{M},\) there is a closed \(\mathcal{M}\)-set
F \subseteq H-D \subseteq A
such that
m(H-D-F)<\frac{1}{2} \varepsilon.
since \(f\) is relatively continuous on \(H-D,\) it is surely so on \(F .\) Moreover,
A-F=(A-(H-D)) \cup(H-D-F);
m(A-F) \leq m(A-(H-D))+m(H-D-F)<\frac{1}{2} \varepsilon+\frac{1}{2} \varepsilon=\varepsilon.
This completes the proof. \(\square\)
Given \([a, b] \subset E^{1}\) and disjoint closed sets \(A, B \subseteq(S, \rho),\) there always is a continuous map \(g : S \rightarrow[a, b]\) such that \(g=a\) on \(A\) and \(g=b\).
If \(A=\emptyset\) or \(B=\emptyset,\) set \(g=b\) or \(g=a\) on all of \(S\).
If, however, \(A\) and \(B\) are both nonempty, set
g(x)=a+\frac{(b-a) \rho(x, A)}{\rho(x, A)+\rho(x, B)}.
As \(A\) is closed, \(\rho(x, A)=0\) iff \(x \in A\) (Problem 15 in Chapter 3, §14); similarly for \(B .\) Thus \(\rho(x, A)+\rho(x, B) \neq 0\).
Also, \(g=a\) on \(A, g=b\) on \(B,\) and \(a \leq g \leq b\) on \(S\).
For continuity, see Chapter 4, §8, Example \((\mathrm{e}) .\) \(\square\)
(Tietze). If \(f :(S, \rho) \rightarrow E^{*}\) is relatively continuous on a closed set \(F \subseteq S,\) there is a function \(g : S \rightarrow E^{*}\) such that \(g=f\) on \(F\),
\inf g[S]=\inf f[F], \sup g[S]=\sup f[F],
and \(g\) is continuous on all of \(S\).
(We assume \(E^{*}\) metrized as in Problem 5 of Chapter 3, §11. If \(|f|<\infty,\) the standard metric in \(E^{1}\) may be used.)
Proof Outline
First, assume inf \(f[F]=0\) and \(\sup f[F]=1 .\) Set
A=F\left(f \leq \frac{1}{3}\right)=F \cap f^{-1}\left[\left[0, \frac{1}{3}\right]\right]
B=F\left(f \geq \frac{2}{3}\right)=F \cap f^{-1}\left[\left[\frac{2}{3}, 1\right]\right].
As \(F\) is closed \(i n S,\) so are \(A\) and \(B\) by Lemma \(2 .\) (Why? \()\)
As \(B \cap A=\emptyset,\) Lemma 3 yields a continuous map \(g_{1} : S \rightarrow\left[0, \frac{1}{3}\right],\) with \(g_{1}=0\) on \(A,\) and \(g_{1}=\frac{1}{3}\) on \(B .\) Set \(f_{1}=f-g_{1}\) on \(F ;\) so \(\left|f_{1}\right| \leq \frac{2}{3},\) and \(f_{1}\) is continuous on \(F .\)
Applying the same steps to \(f_{1}\) (with suitable sets \(A_{1}, B_{1} \subseteq F ),\) find a continuous map \(g_{2},\) with \(0 \leq g_{2} \leq \frac{2}{3} \cdot \frac{1}{3}\) on \(S .\) Then \(f_{2}=f_{1}-g_{2}\) is continuous, and \(0 \leq f_{2} \leq\left(\frac{2}{3}\right)^{2}\) on \(F\).
Continuing, obtain two sequences \(\left\{g_{n}\right\}\) and \(\left\{f_{n}\right\}\) of real functions such that each \(g_{n}\) is continuous on \(S\),
0 \leq g_{n} \leq \frac{1}{3}\left(\frac{2}{3}\right)^{n-1},
and \(f_{n}=f_{n-1}-g_{n}\) is defined and continuous on \(F,\) with
0 \leq f_{n} \leq\left(\frac{2}{3}\right)^{n}
there \(\left(f_{0}=f\right)\).
We claim that
g=\sum_{n=1}^{\infty} g_{n}
is the desired map.
Indeed, the series converges uniformly on \(S\) (Theorem 3 of Chapter 4, §12).
As all \(g_{n}\) are continuous, so is \(g\) (Theorem 2 in Chapter 4, §12). Also,
\left|f-\sum_{k=1}^{n} g_{k}\right| \leq\left(\frac{2}{3}\right)^{n} \rightarrow 0
on \(F(\text { why? }) ;\) so \(f=g\) on \(F .\) Moreover,
0 \leq g_{1} \leq g \leq \sum_{n=1}^{\infty} \frac{1}{3}\left(\frac{2}{3}\right)^{n}=1 \text { on } S.
Hence inf \(g[S]=0\) and \(\sup g[S]=1,\) as required.
Now assume
\inf f[F]=a<\sup f[F]=b \quad\left(a, b \in E^{1}\right)
h(x)=\frac{f(x)-a}{b-a}
so that inf \(h[F]=0\) and \(\sup h[F]=1 .\) (Why?)
As shown above, there is a continuous map \(g_{0}\) on \(S,\) with
g_{0}=h=\frac{f-a}{b-a}
on \(F,\) inf \(g_{0}[S]=0,\) and \(\sup g_{0}[S]=1 .\) Set
a+(b-a) g_{0}=g.
Then \(g\) is the required function. (Verify!)
Finally, if \(a, b \in E^{*}(a<b),\) all reduces to the bounded case by considering \(H(x)=\arctan f(x)\). \(\square\)
(Fréchet). Let \(m : \mathcal{M} \rightarrow E^{*}\) be a strongly regular measure in \((S, \rho) .\) If \(f : S \rightarrow E^{*}\left(E^{n}, C^{n}\right)\) is \(m\) -measurable on \(A,\) then
f=\lim _{i \rightarrow \infty} f_{i}(a \cdot e .(m)) \text { on } A
for some sequence of maps \(f_{i}\) continuous on \(S .\) (We assume \(E^{*}\) to be metrized as in Lemma 4.)
We consider \(f : S \rightarrow E^{*}\) (the other cases reduce to \(E^{1}\) via components).
Taking \(\varepsilon=\frac{1}{i}(i=1,2, \ldots)\) in Theorem \(2,\) we obtain for each \(i\) a closed \(\mathcal{M}\)-set \(F_{i} \subseteq A\) such that
m\left(A-F_{i}\right)<\frac{1}{i}
and \(f\) is relatively continuous on each \(F_{i} .\) We may assume that \(F_{i} \subseteq F_{i+1}\) (if not, replace \(F_{i}\) by \(\bigcup_{k=1}^{i} F_{k} )\).
Now, Lemma 4 yields for each \(i\) a continuous map \(f_{i} : S \rightarrow E^{*}\) such that \(f_{i}=f\) on \(F_{i} .\) We complete the proof by showing that \(f_{i} \rightarrow f\) (pointwise) on the set
B=\bigcup_{i=1}^{\infty} F_{i}
and that \(m(A-B)=0\).
Indeed, fix any \(x \in B .\) Then \(x \in F_{i}\) for some \(i=i_{0},\) hence also for \(i>i_{0}\) (since \(\left\{F_{i}\right\} \uparrow ) .\) As \(f_{i}=f\) on \(F_{i},\) we have
\left(\forall i>i_{0}\right) \quad f_{i}(x)=f(x),
and so \(f_{i}(x) \rightarrow f(x)\) for \(x \in B .\) As \(F_{i} \subseteq B,\) we get
m(A-B) \leq m\left(A-F_{i}\right)<\frac{1}{i}
for all \(i .\) Hence \(m(A-B)=0,\) and all is proved. \(\square\)
This page titled 8.3: Measurable Functions in \((S, \mathcal{M}, m)\) is shared under a CC BY license and was authored, remixed, and/or curated by Elias Zakon (The Trilla Group (support by Saylor Foundation)) .
8.2.E: Problems on Measurable Functions in \((S, \mathcal{M}, m)\)
source[1]-math-19213


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AMOS Customers operating Airbus 320, Airbus 380
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100 MRO Provider AMOS customer that prefers to be undisclosed.
18 Low-Cost Airline
JetSmart Airlines is a South American ultra low-cost carrier created by US investment fund Indigo Partners. JetSmart's primary base of operations is Santiago, Chile.
5 Airline, Regional / Medium Airline
PT Pelita Air Service is a domestic airline based in Jakarta, Indonesia. Its main base is Pondok Cabe Airport.
52 Airline, Large Airline / Flag Carrier
ITA Airways, is the state-owned flag carrier airline of Italy. It is fully owned by the Government of Italy via the Ministry of Economy and Finance. The airline flies scheduled domestic, European, and intercontinental destinations.
65 Low-Cost Airline, Regional / Medium Airline
Flynas is a domestic and international low-cost airline based in Saudi Arabia, the country's first budget airline.
5 Low-Cost Airline
Ultra Air is based in Medellín, Colombia and will be a low-cost operator with an Airbus A320 fleet.
13 Airline, MRO Provider
Bulgaria Air is the flag carrier airline of Bulgaria, with its headquarters at Sofia Airport in Sofia.
Bulgaria Air Technik is providing CAMO services for Bulgaria Air, BUL AIR and AVIO-BRAVO.
Low-Cost Airline
Hong Kong Express Airways is a Hong Kong-based low-cost airline who started operations in 2013.
Gulf Air is a state-owned airline and the flag carrier of the Kingdom of Bahrain.
McDonnell Douglas MD-11
366 Large Airline / Flag Carrier
Lufthansa, is the flag carrier and largest German airline which, when combined with its subsidiaries, is also the largest airline in Europe in terms of passengers carried.
34 Regional / Medium Airline
Tata SIA Airlines Limited, operating as Vistara, is an Indian full-service airline, based in Gurgaon. The carrier is a joint venture between Tata Sons and Singapore Airlines.
80 Large Airline / Flag Carrier, MRO Provider
TAP Air Portugal is the flag carrier airline of Portugal, headquartered at Lisbon Airport. TAP Maintenance & Engineering is the maintenance, repair and operations center of TAP Air Portugal airline.
Israir Airlines is an Israeli airline headquartered in Tel Aviv. It operates domestic scheduled and air taxi flights from Sde Dov Airport, Ben Gurion International Airport, and Eilat Airport, as well as international charter services from Ben Gurion International Airport to Europe and Asia. It also operates VIP flights, and is Israel's third-largest airline.
Air Arabia is a budget airline located at Sharjah International Airport and operates a multi-base business model with hubs in the UAE, Morocco and Egypt.
Air Corsica is a French regional airline which operates passenger services from Corsica to continental France.
Bamboo airways is a Vietnamese start-up airline based in Hanoi.
48 Airline - MRO
Ural Airlines is a Russian airline that operates out of Koltsovo International Airport, Ekaterinburg. With its fleet of 45+ aircraft, the airline serves a Russian and international network.
Ceased operations in the end of 2020.
LaudaMotion was an Austrian Low-Cost Airline that started operations in spring 2018.
Kuwait Airways is the national carrier of Kuwait,with its head office on the grounds of Kuwait International Airport. It operates scheduled international services throughout the Middle East, to the Indian subcontinent, Europe, Southeast Asia and North America.
Viva Aerobus is a Latin America low cost airline which operates a modern fleet of A320.
Ceased operations in 2019.
EGYPTAIR is the flag carrier airline of Egypt. The airline is based at Cairo International Airport, its main hub, operating scheduled passenger and freight services to more than 75 destinations in the Middle East, Europe, Africa, Asia, and the Americas.
Diamond DA-20
Mooney M20R
Tecnam P2002
6 CAMO
AMROS-Global is a Swiss independent advisor to the aviation and aerospace industry handling all aspects of technical, operational and asset management of aircraft.
20 Airline
Air Serbia is the flag carrier and largest airline of Serbia. The airline has its hub at Belgrade Nikola Tesla Airport.
Ceased operations in 2018
7 Regional / Medium Airline
Nile Air is an Egyptian airline based at Cairo International Airport that operates scheduled services to destinations in Egypt and the Middle East using a small fleet of Airbus A320-200s.
Etihad Airways is a flag carrier and the second-largest airline of the United Arab Emirates. Its head office is in Khalifa City, Abu Dhabi.
Iberia is the leading carrier on routes between Europe and Latin America and together with its subsidiary Iberia Express and its franchise partner Iberia Regional/Air Nostrum, it operates about 600 flights each day with a fleet of 136 aircraft.
7 Regional / Medium Airline AMOS customer that prefers to be undisclosed.
DHC-8
Olympic Air is a regional Greek airline and subsidiary of the airline carrier Aegean Airlines.
23 Large Airline / Flag Carrier
PAL Express is a subsidiary airline under the ownership of Philippine Airlines. It is PAL's regional division, with services from its hubs in Manila, Clark, Cebu and Davao.
123 Low-Cost Airline
Vueling Airlines is a Spanish low-cost airline headquartered in Barcelona. Vueling serves over 100 destinations in Africa, Asia and Europe and is currently the second largest airline in Spain.
Oman Air is the national airline of Oman. Based on the grounds of Muscat International Airport in Seeb, Muscat, it operates scheduled domestic and international passenger services, as well as regional air taxi and charter flights.
Aeroflot is the flag carrier and largest airline of the Russian Federation. Being one of the oldest airlines in the world, it operates domestic and international passenger services, mainly from its hub at Sheremetyevo International Airport, Moscow.
Headquartered at Stockholm Arlanda Airport, Scandinavian Airlines is the flag carrier of Denmark, Norway and Sweden and the largest airline in Scandinavia. Founded in the 40s, the airline offers domestic and international flights to around 90 destinations
Lacsa is the national airline of Costa Rica and is based in San José. It operates international scheduled services to over 35 destinations in Central, North and South America. It is part of Grupo TACA.
Avianca is headquartered in Bogotá, and the flag carrier of Colombia. Avianca is the largest airline in Colombia and has the most extended network of destinations in the Americas and one of the largest and most modern aircraft fleet in the continent.
TACA Peru is an airline based in Lima, Peru. It operates domestic services and international services. It is part of Grupo AVIANCATACA and operates its flights with TACA's codes.
AeroGal (Avianca Ecuador) is an airline based in Quito, Ecuador. It operates passenger and cargo flights within Ecuador, between the mainland and the Galápagos Islands, and between Ecuador and New York, Peru (on behalf of TACA) and Colombia.
TACA is the flag-carrier of El Salvador. It links the Americas together through its four Hubs and its extensive route network from Canada to Brazil, flying to 50 destinations in 22 countries.
Cebu Pacific is a Philippine Low Cost Carrier being founded in 1996. Today, Cebu Pacific operates flights to around 60 destinations.
VietJet Air is a low-cost airline based in Hanoi, Vietnam. Celebrating its maiden flight in December 2011, VietJet is the first private airline in Vietnam to be licensed to operate domestic and international flights.
Pegasus Airlines is a Turkish low-cost airline that operates from the Sabiha Gökçen airport in Istanbul. The airline serves a route network of more than 26 countries, 62 destinations.
56 Charter Airline
Besides the long-term customers Thomas Cook Belgium, Condor Berlin and Condor Flugdienst, also the remaining members of the Thomas Cook Group (TC UK and Scandinavia) are relying on AMOS since 2012.
156 MRO Provider
Saudia Aerospace Engineering Industries (SAEI) is a subsidiary of Saudi Arabian Airlines. More than 130 AC of Saudi Arabian Airlines are fully maintained by SAEI. The MRO provider has more than 5'200 employees and will expand its MRO facilities in Jeddah.
Brussels Airlines, the flag carrier of Belgium offers flights from its base at Brussels Airport to Europe and Africa.
SAA Technical (SAAT) is the largest full-service maintenance, repair and overhaul organisation on the African continent. Fully FAA-certified since the early 1990's, SAAT serves an increasing number of local, regional and international airlines.
Finnair Technical Services, as the maintenance organisation of Finnair, is based at Helsinki Airport. The Finnish maintenance provider's core business is aircraft and component repair and overhaul.
4 Medium Airline
Ceased operations. Dakar based Senegal Airlines, the flag carrier of Senegal, launched operations of its Airbus 320s in the beginning of 2011. Senegal Airlines used to connect the West-African destinations Abidjan, Bamako, Banjul, Conakry, Nouakchott and Ouagadougou.
StarFlyer Inc. is a low-cost carrier based in Kitakyushu, Japan. It is modeled as a "low-cost, high-quality" carrier aimed at business and leisure travelers.
Royal Brunei Airlines is the flag carrier airline of the Sultanate of Brunei with its homebase at the Brunei International Airport in Berakas. The airline offers its customers around 20 destinations in Asia, Europe and Oceania.
Wizz Air, established in 2003, provides low-cost air transport to and from Central and Eastern Europe. The Hungarian based airlines currently offers flights on over 150 routes in Europe.
Ceased operations.
Alitalia is the new Italian flag airline and started its operations early 2009 with the merger of Air One and Alitalia. Being the largest domestic airline in Italy, Alitalia offers its customers around 80 European and international destinations.
STC Russia is the largest state-owned airline in Russia and one of the leading Russian airlines with around 3 million passengers per year. The airline operates scheduled and charter passenger flights from St. Petersburg and its main hub Moscow.
Jetstar Pacific Airlines, part of the Jetstar LCC network, is a low-cost airline based in Ho Chi Minh City, Vietnam. Jetstar Pacific Airlines focuses on domestic Vietnamese and regional routes from its main hub.
easyJet is a low cost airline based at London Luton Airport. It is one of the largest low-fare airlines in Europe, operating domestic and international scheduled services 600 routes in almost 40 countries.
Condor is one of the largest holiday airlines in Europe. Based in Frankfurt/Germany, the newly-established Condor Technik GmbH is responsible for the maintenance and overhaul of the Boeing 757/767 fleets of Condor Flugdienst GmbH.
Aegean Airlines is based in Athens/Greece and operates around 40 domestic and international routes. As new A320s will replace the older aircraft, Aegean will soon have the youngest fleet in the region of Balkans and South-East Europe.
Since AirAsia introduced its low fare, no frills concept in December 2001, the Malaysian airline now flies to around 100 destinations.
IndiGo is an Indian nation-wide low-cost airline. The airline is a subsidiary of InterGlobe Enterprises, the foremost travel conglomerate in India, and operates a fleet of brand-new Airbus A320 family aircraft.
6 Airline
Irish low-fare point to point carrier Aer Lingus operates domestic and international passenger and cargo services.
Eurowings is the Lufthansa Group's low-cost airline and as such part of the world's largest aviation group. The German airline specialises in budget-priced direct flights within Europe but also flies to long-haul destinations in America, Asia and the Caribbean.
25 MRO Provider
ST Engineering is a leading MRO provider in Asia.
7 Charter Airline
Austrian Airlines Group based in Vienna, Austria operating scheduled services to more than 130 destinations on all five continents.
Merged with Condor Flugdienst GmbH in July 2016.
ceased operations
Bombardier CS300
Swiss International Air Lines is the flag carrier of Switzerland, operating scheduled services to destinations in the Americas, Europe, Africa, Asia and Middle East.
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Regulators have allowed "dead dog zombie" superannuation funds to underperform for more than a decade without enforcement, according to former Australian Securities & Investments Commission counsel Pamela Hanrahan, who has called for a specialist regulator to take charge of the $2.6 trillion nest egg system.
At a hearing for the Productivity Commission's review of superannuation in Sydney yesterday, Professor Hanrahan said the current disclosure obligations regime that dominated financial regulation was not protecting consumers.
"That framework … may well be coming to the end of its life. It may well have proved to be a failed experiment in some extent," Professor Hanrahan said.
"The current disclosure requirements — it's full of information that is not meaningful to members and it's provided at the wrong time," she said.
Professor Hanrahan, an expert adviser to the banking royal commission and the former head of the investment managers stakeholders team at ASIC, which dealt with the aftermath of the 2009 Trio collapse, said super members were often confronted with too much choice. There were some 40,000 super investment options in the for-profit choice segment.
"At the point where an individual member is required to make a choice I don't think they are well supported by mandatory disclosure or the advice laws at the moment," Professor Hanrahan said.
There was friction between what ASIC was responsible for in the super system and what was the responsibility of the Australian Prudential Regulation Authority.
"(ASIC) is a financial markets regulator but it's also a consumer regulator. Sometimes within ASIC there is a bit of tension between those two roles," she said, noting that ASIC often treated superannuation members as investors rather than consumers.
Professor Hanrahan said while the Productivity Commission assumed the "current regulatory architecture" was immovable, she suggested the department's final response should aim to shake this up. She floated the idea of a "dedicated pensions fund regulator" or "a specialist consumer regulator for the financial sector".
"I worked on Trio and that was an interesting exercise in (regulatory) agency co- operation. There is a kind of a sense that people are often surprised at how lenient the performance standards in the industry are," she said.
"A law firm will say it's a very high threshold for duty of care (obligations), but the conduct has to be pretty egregious before a successful action can be run. Even though there's a lot of regulator interest in the space, when you drill down and say: if you've got a board of trustees that has woefully unperformed for a decade, it couldn't possibly be in members' interests to let this dead dog zombie thing keep lurching along.
The Productivity Commission's draft report on superannuation found entrenched overcharging in the for-profit fund sector, underperforming trade union funds that refuse to merge despite it being in their members' best interests, and an industry happy to preside over a system that acts as an "unlucky lottery" for many savers.
The draft report said APRA and ASIC "need to become member champions — confidently and effectively policing trustee conduct".