Question

Fubinis Theorem for Lebesgue Integrals

score 62 · Answer 1 · 2023-11-23 17:51:38

62

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Fubinis Theorem for Lebesgue Integrals

Published on 23 Nov 2023 - 17:51

score 136 · Answer 2 · 2023-11-24 03:08:06

136

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Prove that $ \lim_{p\rightarrow 0^+}(\frac{1}{|E|}\int_E f^p)^{\frac{1}{p}}=\exp(\frac{1}{|E|}\int_E \log f) $

Published on 24 Nov 2023 - 3:08

score 59 · Answer 3 · 2026-04-12 07:43:04

59

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Locally essentially bounded function is locally integrable

Published on 12 Apr 2026 - 7:43

score 88 · Answer 4 · 2026-04-10 18:11:26

88

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Integral over some measure is the same as integrating over the measure of the preimages of some intervals

Published on 10 Apr 2026 - 18:11

score 52 · Answer 5 · 2026-04-12 12:47:17

52

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Is this calculation of an area correct?

Published on 12 Apr 2026 - 12:47

score 35 · Answer 6 · 2026-04-12 00:29:58

35

Views

How to show that an absolutely continuous increasing real function is an indefinite integral of an L1 function

Published on 12 Apr 2026 - 0:29

score 37 · Answer 7 · 2026-04-12 09:33:10

37

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$\frac{f}{|x|^4+1}$ lies in $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ for $f \in L^2(\mathbb{R}^n)$ and $n > 6$

Published on 12 Apr 2026 - 9:33

score 62 · Answer 8 · 2023-11-27 10:21:01

62

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Is the function $f(x)=x^{2} \chi_{[-1,1] \backslash \mathbb{Q}}(x)$ $\mathcal{L}^{1}$-integrable?

Published on 27 Nov 2023 - 10:21

score 71 · Answer 9 · 2026-04-12 10:36:06

71

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Ambiguity in the definition of a simple function

Published on 12 Apr 2026 - 10:36

score 63 · Answer 10 · 2026-04-07 12:51:58

63

Views

Example of a function $f(x,t)$ such that $t \to \int f(x,t) dx$ and $\int f(x,t) dxdt$ finite, BUT $\int \lvert f(x,t) \rvert dxdt =\infty$?

Published on 07 Apr 2026 - 12:51

score 50 · Answer 11 · 2026-04-11 07:29:41

50

Views

Are negative powers of cosine Lebesgue-integrable?

Published on 11 Apr 2026 - 7:29

score 51 · Answer 12 · 2026-04-10 23:23:21

51

Views

Lebesgue integral to get cumulative distribution function of random variable

Published on 10 Apr 2026 - 23:23

score 159 · Answer 13 · 2026-04-12 17:43:05

159

Views

Integral inequality for $|f(x)|^2$ and $|\nabla f|$ in $\mathbb{R}^2$

Published on 12 Apr 2026 - 17:43

score 136 · Answer 14 · 2023-11-30 21:54:42

136

Views

non-negative $\{f_n\}$ such that $\int f_{n}d\mu=1$ but not $f_{n}/n \to 0$ a.e.

Published on 30 Nov 2023 - 21:54

score 46 · Answer 15 · 2026-04-13 11:59:43

46

Views

For Lebesgue integral theory, whether an integrable sequence of functions converging a.e. converges in L1 under a given "integral finite condition"

Published on 13 Apr 2026 - 11:59

List Question

Fubinis Theorem for Lebesgue Integrals

Prove that $ \lim_{p\rightarrow 0^+}(\frac{1}{|E|}\int_E f^p)^{\frac{1}{p}}=\exp(\frac{1}{|E|}\int_E \log f) $

Locally essentially bounded function is locally integrable

Integral over some measure is the same as integrating over the measure of the preimages of some intervals

Is this calculation of an area correct?

How to show that an absolutely continuous increasing real function is an indefinite integral of an L1 function

$\frac{f}{|x|^4+1}$ lies in $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ for $f \in L^2(\mathbb{R}^n)$ and $n > 6$

Is the function $f(x)=x^{2} \chi_{[-1,1] \backslash \mathbb{Q}}(x)$ $\mathcal{L}^{1}$-integrable?

Ambiguity in the definition of a simple function

Example of a function $f(x,t)$ such that $t \to \int f(x,t) dx$ and $\int f(x,t) dxdt$ finite, BUT $\int \lvert f(x,t) \rvert dxdt =\infty$?

Are negative powers of cosine Lebesgue-integrable?

Lebesgue integral to get cumulative distribution function of random variable

Integral inequality for $|f(x)|^2$ and $|\nabla f|$ in $\mathbb{R}^2$

non-negative $\{f_n\}$ such that $\int f_{n}d\mu=1$ but not $f_{n}/n \to 0$ a.e.

For Lebesgue integral theory, whether an integrable sequence of functions converging a.e. converges in L1 under a given "integral finite condition"

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