Question

Cauchy in measure question

score 668 · Answer 1 · 2026-04-08 12:36:22

668

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Cauchy in measure question

Published on 08 Apr 2026 - 12:36

score 60 · Answer 2 · 2026-04-08 02:45:07

60

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A question about $L^p$ spaces

Published on 08 Apr 2026 - 2:45

score 62 · Answer 3 · 2017-01-01 14:50:02

62

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Construct a measurable subset E such that $\lim_{\delta \to 0}\frac{1}{2\delta}\int_{p+\delta}^{p-\delta}\chi_E(x)dx=a$

Published on 01 Jan 2017 - 14:50

score 108 · Answer 4 · 2017-01-01 18:09:06

108

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Does there exist a measurable subset $E$ such that $\varepsilon < \frac{|E\cap{I}|}{I} < 1-\varepsilon$ for every finite interval I =[a,b]?

Published on 01 Jan 2017 - 18:09

score 250 · Answer 5 · 2017-01-01 18:32:56

250

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$g(x)=\sin(\frac{1}{x}) , g(0)=0$ Define $G(x)=\int _{0}^{x}g\left( t\right) dt$ . Is $0$ a Lebesgue point of g?

Published on 01 Jan 2017 - 18:32

score 268 · Answer 6 · 2017-01-02 02:14:52

268

Views

Writing integration over abstract measure space as integration over $\mathbb{R}$

Published on 02 Jan 2017 - 2:14

score 174 · Answer 7 · 2017-01-02 10:44:10

174

Views

Limit of integral converges to esssup

Published on 02 Jan 2017 - 10:44

score 86 · Answer 8 · 2017-01-02 11:35:28

86

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Is the set $F$ make the $M_{\lambda}(0)$ finite?

Published on 02 Jan 2017 - 11:35

score 454 · Answer 9 · 2026-02-23 03:58:10

454

Views

Amenable group $G$ and a (left) invariant mean on it.

Published on 23 Feb 2026 - 3:58

score 28 · Answer 10 · 2026-04-07 23:48:56

28

Views

An integral problem with the measure of a set in the integrand

Published on 07 Apr 2026 - 23:48

score 212 · Answer 11 · 2017-01-03 10:09:33

212

Views

Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$

Published on 03 Jan 2017 - 10:09

score 47 · Answer 12 · 2017-01-03 13:35:05

47

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Calculate $\lim_{m \rightarrow \infty} \int_{[0, 1]} f_m(x) d\lambda(x)$.

Published on 03 Jan 2017 - 13:35

score 26 · Answer 13 · 2017-01-03 16:22:38

26

Views

Question about integral inequality

Published on 03 Jan 2017 - 16:22

score 83 · Answer 14 · 2026-04-01 22:14:38

83

Views

Finite expectation implies absolutely convergent?

Published on 01 Apr 2026 - 22:14

score 292 · Answer 15 · 2017-01-03 21:31:34

292

Views

Question 10 chapter 11 of Principles of Mathematical Analysis of Rudin, W.

Published on 03 Jan 2017 - 21:31

List Question

Cauchy in measure question

A question about $L^p$ spaces

Construct a measurable subset E such that $\lim_{\delta \to 0}\frac{1}{2\delta}\int_{p+\delta}^{p-\delta}\chi_E(x)dx=a$

Does there exist a measurable subset $E$ such that $\varepsilon < \frac{|E\cap{I}|}{I} < 1-\varepsilon$ for every finite interval I =[a,b]?

$g(x)=\sin(\frac{1}{x}) , g(0)=0$ Define $G(x)=\int _{0}^{x}g\left( t\right) dt$ . Is $0$ a Lebesgue point of g?

Writing integration over abstract measure space as integration over $\mathbb{R}$

Limit of integral converges to esssup

Is the set $F$ make the $M_{\lambda}(0)$ finite?

Amenable group $G$ and a (left) invariant mean on it.

An integral problem with the measure of a set in the integrand

Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$

Calculate $\lim_{m \rightarrow \infty} \int_{[0, 1]} f_m(x) d\lambda(x)$.

Question about integral inequality

Finite expectation implies absolutely convergent?

Question 10 chapter 11 of Principles of Mathematical Analysis of Rudin, W.

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