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Integral involving distance function

score 286 · Answer 1 · 2026-04-13 07:05:05

286

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Integral involving distance function

Published on 13 Apr 2026 - 7:05

score 39 · Answer 2 · 2026-04-14 16:48:45

39

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How to show $\int_{-1}^{1}\frac{1}{\lambda-f(x)}dx $ is not integrable if $f$ is continuous and $\lambda$ is in the image of $f$

Published on 14 Apr 2026 - 16:48

score 360 · Answer 3 · 2026-03-31 03:26:56

360

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Proving Tonelli's Theorem for $n$ Factors

Published on 31 Mar 2026 - 3:26

score 71 · Answer 4 · 2026-04-10 23:07:54

71

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Relating arbitrary measure with Lebesgue measure

Published on 10 Apr 2026 - 23:07

score 62 · Answer 5 · 2026-04-11 02:40:37

62

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Integrating multiple of two measurable functions

Published on 11 Apr 2026 - 2:40

score 127 · Answer 6 · 2026-03-20 02:14:22

127

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Show that $e^{-|x|^\alpha}$ is $\lambda^d$ integrable for every $\alpha>0$

Published on 20 Mar 2026 - 2:14

score 71 · Answer 7 · 2026-04-08 20:57:57

71

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Does order matter when integrating with product measures?

Published on 08 Apr 2026 - 20:57

score 142 · Answer 8 · 2026-05-05 00:07:28

142

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$L^2$ convergence over $[0,T] \times \Omega$ for all $T>0$ implies convergence a.e. for a subsequence over $[0,\infty) \times \Omega$

Published on 05 May 2026 - 0:07

score 163 · Answer 9 · 2026-05-15 00:11:27

163

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The notion of a point of vanishing mean oscillation is more general than that of Lebesgue points.

Published on 15 May 2026 - 0:11

score 118 · Answer 10 · 2026-03-20 13:29:46

118

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Interchanging two integrals with different measures.

Published on 20 Mar 2026 - 13:29

score 111 · Answer 11 · 2026-05-05 01:11:16

111

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An example of Sobolev function.

Published on 05 May 2026 - 1:11

score 445 · Answer 12 · 2026-05-15 00:10:27

445

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Lebesgue point - an example

Published on 15 May 2026 - 0:10

score 431 · Answer 13 · 2026-04-12 04:30:40

431

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Does the derivative of a differentiable function have to be Lebesgue integrable in some interval?

Published on 12 Apr 2026 - 4:30

score 248 · Answer 14 · 2026-04-13 00:16:45

248

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If $f$ is a continuous function with compact support, then $\lim\limits_{h\to\infty}\int_{\mathbb{R}}|f(x-h)+f(x)|dx=2\int_{\mathbb{R}}|f(x)|dx$

Published on 13 Apr 2026 - 0:16

score 74 · Answer 15 · 2026-04-13 09:25:27

74

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How to rewrite integral of L^2 function and conclude about convergence of series

Published on 13 Apr 2026 - 9:25

List Question

Integral involving distance function

How to show $\int_{-1}^{1}\frac{1}{\lambda-f(x)}dx $ is not integrable if $f$ is continuous and $\lambda$ is in the image of $f$

Proving Tonelli's Theorem for $n$ Factors

Relating arbitrary measure with Lebesgue measure

Integrating multiple of two measurable functions

Show that $e^{-|x|^\alpha}$ is $\lambda^d$ integrable for every $\alpha>0$

Does order matter when integrating with product measures?

$L^2$ convergence over $[0,T] \times \Omega$ for all $T>0$ implies convergence a.e. for a subsequence over $[0,\infty) \times \Omega$

The notion of a point of vanishing mean oscillation is more general than that of Lebesgue points.

Interchanging two integrals with different measures.

An example of Sobolev function.

Lebesgue point - an example

Does the derivative of a differentiable function have to be Lebesgue integrable in some interval?

If $f$ is a continuous function with compact support, then $\lim\limits_{h\to\infty}\int_{\mathbb{R}}|f(x-h)+f(x)|dx=2\int_{\mathbb{R}}|f(x)|dx$

How to rewrite integral of L^2 function and conclude about convergence of series

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