Question

Example of decreasing sequence of sets with first set having infinite measure

score 3.6k · Answer 1 · 2026-04-12 16:46:04

3.6k

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Example of decreasing sequence of sets with first set having infinite measure

Published on 12 Apr 2026 - 16:46

score 91 · Answer 2 · 2026-04-25 01:01:10

91

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Show that $\int f_2(x)dx=\frac{1}{2}\int f(x)dx$ if $f_2(x)=f(2x)$.

Published on 25 Apr 2026 - 1:01

score 329 · Answer 3 · 2026-04-16 09:06:47

329

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Prove that $\limsup_{n\to\infty}\int f_n\leq \int\limsup_{n\to\infty }f_n$

Published on 16 Apr 2026 - 9:06

score 58 · Answer 4 · 2026-04-14 08:19:04

58

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Convergence in $L^p(\Omega)$ implies convergence of integral

Published on 14 Apr 2026 - 8:19

score 83 · Answer 5 · 2026-04-25 00:56:07

83

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How to prove this integral inequality

Published on 25 Apr 2026 - 0:56

score 697 · Answer 6 · 2026-04-16 19:02:54

697

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Show that the graph of a function is measurable.

Published on 16 Apr 2026 - 19:02

score 96 · Answer 7 · 2026-04-11 09:10:45

96

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Proof about σ-algebra

Published on 11 Apr 2026 - 9:10

score 345 · Answer 8 · 2026-04-25 00:56:07

345

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A Lebesgue integral problem that seems very intuitive!

Published on 25 Apr 2026 - 0:56

score 36 · Answer 9 · 2026-04-15 18:44:49

36

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$f_{n}$ sequence of measurable functions on measurable set $E$, and $E_{0}$ the set of $x \in E$ that $f_{n}$ converges. Then $E_{0}$ is measurable.

Published on 15 Apr 2026 - 18:44

score 44 · Answer 10 · 2015-10-25 01:46:29

44

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Determine if the collection of set formed by element by element union,intersection and set difference of two sigma algebra is a sigma algebra

Published on 25 Oct 2015 - 1:46

score 440 · Answer 11 · 2026-04-15 21:36:18

440

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Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.

Published on 15 Apr 2026 - 21:36

score 2.1k · Answer 12 · 2026-04-14 15:54:28

2.1k

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Show (using Vitali Covering Lemma) that the union of any collection of closed, bounded non-generate intervals is measurable.

Published on 14 Apr 2026 - 15:54

score 365 · Answer 13 · 2026-04-25 00:56:23

365

Views

Application of Differentiation using Lebesgue Dominated Convergence Theorem

Published on 25 Apr 2026 - 0:56

score 345 · Answer 14 · 2026-04-11 21:51:10

345

Views

Lebesgue and counting measure not interchangeble in integral and integrand?

Published on 11 Apr 2026 - 21:51

score 40 · Answer 15 · 2026-04-14 09:37:33

40

Views

Is this result in general true for lebesgue measurable sets

Published on 14 Apr 2026 - 9:37

List Question

Example of decreasing sequence of sets with first set having infinite measure

Show that $\int f_2(x)dx=\frac{1}{2}\int f(x)dx$ if $f_2(x)=f(2x)$.

Prove that $\limsup_{n\to\infty}\int f_n\leq \int\limsup_{n\to\infty }f_n$

Convergence in $L^p(\Omega)$ implies convergence of integral

How to prove this integral inequality

Show that the graph of a function is measurable.

Proof about σ-algebra

A Lebesgue integral problem that seems very intuitive!

$f_{n}$ sequence of measurable functions on measurable set $E$, and $E_{0}$ the set of $x \in E$ that $f_{n}$ converges. Then $E_{0}$ is measurable.

Determine if the collection of set formed by element by element union,intersection and set difference of two sigma algebra is a sigma algebra

Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.

Show (using Vitali Covering Lemma) that the union of any collection of closed, bounded non-generate intervals is measurable.

Application of Differentiation using Lebesgue Dominated Convergence Theorem

Lebesgue and counting measure not interchangeble in integral and integrand?

Is this result in general true for lebesgue measurable sets

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