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Durret Example 1.7.4: problem guidance

score 189 · Answer 1 · 2020-07-06 05:17:53

189

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Durret Example 1.7.4: problem guidance

Published on 06 Jul 2020 - 5:17

score 80 · Answer 2 · 2020-07-08 11:05:05

80

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Using Fubini to prove $p\int_t^\infty\frac1{s^{p+1}}(\int_0^s w(x) \, dx) \, ds=\int_t^\infty\frac{w(s)}{s^p} \, ds+\frac{\int_0^tw(x) \, dx}{t^p}$

Published on 08 Jul 2020 - 11:05

score 194 · Answer 3 · 2020-07-13 16:16:38

194

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Proving that the triple integral can be evaluated by iterated integrals

Published on 13 Jul 2020 - 16:16

score 55 · Answer 4 · 2026-04-11 12:59:27

55

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Integral Identity on Measure Theory

Published on 11 Apr 2026 - 12:59

score 2.7k · Answer 5 · 2026-03-28 22:28:22

2.7k

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Why exactly can you change the order of integration in a double (and triple) integral?

Published on 28 Mar 2026 - 22:28

score 71 · Answer 6 · 2026-04-08 20:58:53

71

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Understanding the double integral $\int_0^\infty\int_0^t f(x)g(t-x)dxdt$

Published on 08 Apr 2026 - 20:58

score 72 · Answer 7 · 2026-03-28 23:55:54

72

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A very tangled example with delta function

Published on 28 Mar 2026 - 23:55

score 37 · Answer 8 · 2026-04-07 05:40:21

37

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Rewrite $\int_{\mathbb{R^4}}\int_{\mathbb{R^4}}\ h(|x|^2,|y|^2,x\cdot y)\ dx\ dy$ as $\int\int\limits_{\Omega}\int\ J(u,v,w)\ h(u,v,w)\ du\ dv\ dw$.

Published on 07 Apr 2026 - 5:40

score 894 · Answer 9 · 2026-03-26 04:28:50

894

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Fubini's theorem for integrable functions.

Published on 26 Mar 2026 - 4:28

score 76 · Answer 10 · 2026-04-12 23:11:25

76

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Lemma 6.2 Lee's Introduction to Smooth Manifolds

Published on 12 Apr 2026 - 23:11

score 44 · Answer 11 · 2026-03-29 13:24:20

44

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Calculate $ \int \limits_{V}\left(x^{2}+y^{2}\right) d(x, y, z) $, where $V$ is limited by the areas $ x^{2}+y^{2}= $ $ 2 z $ and $ z=2 $.

Published on 29 Mar 2026 - 13:24

score 139 · Answer 12 · 2026-04-11 23:54:54

139

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Fubini's theorem in Lebesgue integral theory. Incomprehensible point in the proof by Axler.

Published on 11 Apr 2026 - 23:54

score 117 · Answer 13 · 2026-03-25 22:10:51

117

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How to use Hölder inequality to prove this integral inequality?

Published on 25 Mar 2026 - 22:10

score 103 · Answer 14 · 2023-03-22 15:23:41

103

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Interchanging expectation and integration with a collection of random integrands

Published on 22 Mar 2023 - 15:23

score 31 · Answer 15 · 2026-03-30 12:26:03

31

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How do I take an expectation over a continuum of iid random variables?

Published on 30 Mar 2026 - 12:26

List Question

Durret Example 1.7.4: problem guidance

Using Fubini to prove $p\int_t^\infty\frac1{s^{p+1}}(\int_0^s w(x) \, dx) \, ds=\int_t^\infty\frac{w(s)}{s^p} \, ds+\frac{\int_0^tw(x) \, dx}{t^p}$

Proving that the triple integral can be evaluated by iterated integrals

Integral Identity on Measure Theory

Why exactly can you change the order of integration in a double (and triple) integral?

Understanding the double integral $\int_0^\infty\int_0^t f(x)g(t-x)dxdt$

A very tangled example with delta function

Rewrite $\int_{\mathbb{R^4}}\int_{\mathbb{R^4}}\ h(|x|^2,|y|^2,x\cdot y)\ dx\ dy$ as $\int\int\limits_{\Omega}\int\ J(u,v,w)\ h(u,v,w)\ du\ dv\ dw$.

Fubini's theorem for integrable functions.

Lemma 6.2 Lee's Introduction to Smooth Manifolds

Calculate $ \int \limits_{V}\left(x^{2}+y^{2}\right) d(x, y, z) $, where $V$ is limited by the areas $ x^{2}+y^{2}= $ $ 2 z $ and $ z=2 $.

Fubini's theorem in Lebesgue integral theory. Incomprehensible point in the proof by Axler.

How to use Hölder inequality to prove this integral inequality?

Interchanging expectation and integration with a collection of random integrands

How do I take an expectation over a continuum of iid random variables?

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