# stephen

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|          |                | bio     | visits   |                 |          |
|----------|----------------|---------|----------|-----------------|----------|
|          | 106 reputation | website |          | member for      | 5 months |
| 6 badges | location       |         | seen     | Jan 11 at 21:34 |          |

# 38 Actions

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| Dec23 | awarded  | Tumbleweed                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |
| Dec16 | accepted | Absolutely continuous functions with derivatives in $L^p$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
| Dec16 | asked    | On a question about the Haar measure                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |
| Dec15 | awarded  | Teacher                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
| Dec15 | comment  | Absolutely continuous functions with derivatives in $L^p$@Jonas. Yes you are totally right. It is integrable on bounded intervals, and this is what I use for the proof. Sorry for my confusion!                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| Dec15 | revised  | Absolutely continuous functions with derivatives in $L^p$added 8 characters in body                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
| Dec15 | comment  | Absolutely continuous functions with derivatives in $L^p$@Jonas. Yes thank you!                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |
| Dec15 | answered | Absolutely continuous functions with derivatives in $L^p$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
| Dec15 | comment  | Absolutely continuous functions with derivatives in $L^p$...is integrable, and we have $F(b)-F(a)= \int_a^b F'(x)dx$. I will post an answer to my question so that you will understand the discussion between Giuseppe and I.                                                                                                                                                                                                                                                                                                                                                                                                                                             |
| Dec15 | comment  | Absolutely continuous functions with derivatives in $L^p$@Jonas: The problem comes from a problems set that our professor gave us to practise for the final exam. I am not sure where she took them from. The definition of absolutely continuous function that I use is: For every $\epsilon>0$, there exists $\delta > 0$ such that for any finite collection of disjoint intervals $(a_i, b_i)_{i=1}^n$, $\sum_i |F(b_i)-F(a_i)|<\epsilon$ whenever $\sum_i (b_i-a_i) < \delta$. This is the definition from Folland's real analysis. The Fundamental theorem of calculus states that $F$ is absolutely continuous if and only if $F'$ exists almost everywhere and... |
| Dec14 | awarded  | Commentator                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
| Dec14 | comment  | Absolutely continuous functions with derivatives in $L^p$@Jonas. Is it important in this case?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |
| Dec14 | comment  | Absolutely continuous functions with derivatives in $L^p$@Jonas. It is not directly part of my definition, but it follows from the fundamental theorem of calculus for Lebesgue integration.                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
| Dec13 | accepted | “Commutativity” of integrals                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
| Dec13 | asked    | “Commutativity” of integrals                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
| Dec12 | comment  | Absolutely continuous functions with derivatives in $L^p$Oh if you take $L = \int_{\mathbb R} f'(t) dt$, then I think it works applying Holder.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |
| Dec12 | comment  | Absolutely continuous functions with derivatives in $L^p$I thought about that. Then doesn't the constant $L$ that you get depend on $x$ and $y$?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| Dec12 | revised  | Absolutely continuous functions with derivatives in $L^p$added 15 characters in body                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |
| Dec12 | asked    | Absolutely continuous functions with derivatives in $L^p$                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
| Dec11 | accepted | How to know a function is in $L^p$.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
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