network profile
| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 5 months |
| seen | Jan 11 at 21:34 | |
| stats | profile views | 16 |
|
Dec 23 |
awarded | Tumbleweed |
|
Dec 16 |
accepted | Absolutely continuous functions with derivatives in $L^p$ |
|
Dec 16 |
asked | On a question about the Haar measure |
|
Dec 15 |
awarded | Teacher |
|
Dec 15 |
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! |
|
Dec 15 |
revised |
Absolutely continuous functions with derivatives in $L^p$ added 8 characters in body |
|
Dec 15 |
comment |
Absolutely continuous functions with derivatives in $L^p$ @Jonas. Yes thank you! |
|
Dec 15 |
answered | Absolutely continuous functions with derivatives in $L^p$ |
|
Dec 15 |
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. |
|
Dec 15 |
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... |
|
Dec 14 |
awarded | Commentator |
|
Dec 14 |
comment |
Absolutely continuous functions with derivatives in $L^p$ @Jonas. Is it important in this case? |
|
Dec 14 |
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. |
|
Dec 13 |
accepted | “Commutativity” of integrals |
|
Dec 13 |
asked | “Commutativity” of integrals |
|
Dec 12 |
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. |
|
Dec 12 |
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 $y$? |
|
Dec 12 |
revised |
Absolutely continuous functions with derivatives in $L^p$ added 15 characters in body |
|
Dec 12 |
asked | Absolutely continuous functions with derivatives in $L^p$ |
|
Dec 11 |
accepted | How to know a function is in $L^p$. |
