List questions from lebesgue-measure

Published on 12 Apr 2026 - 2:23

312

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Let $\alpha \in (0,1)$. Find a Borel subset $E$ of $[-1,1]$ s.t. $\lim_{r\to 0^{+}} \frac{m(E\cap [-r,r])}{2r}=\alpha.$

Published on 09 Dec 2019 - 22:07

889

Views

Proving the Lebesgue measure space completes the Borel measure space

Published on 25 Mar 2026 - 10:56

164

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Measure Theoretic rigorous formulation/definition of the Expectation Maximization algorithm (EM Algorithm)

Published on 12 Apr 2026 - 6:20

269

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Sard's Theorem with whatever function

Published on 10 Apr 2026 - 18:18

64

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Prove that there exists no Lebesgue-measurable set $A$ such that for every interval $I$ the Lebesgue measure of $A\cap I$ is half the length of $I$.

Published on 10 Dec 2019 - 21:09

190

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A variation of Borel-Cantelli Lemma 2

Published on 26 Mar 2026 - 1:16

24

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I want to raise a question about the notation of Dini derivatives

Published on 09 Apr 2026 - 12:53

57

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$g_n(x)=f(x+1/n)$ converges to $f$ in $L^1(\mathbb{R}$

Published on 03 Apr 2026 - 22:07

700

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Example of non measurable function in $\mathbb R^2$

Published on 28 Mar 2026 - 13:35

88

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Open intervals as union of closed intervals

Published on 28 Mar 2026 - 10:16

68

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Measures of subsets of a measurable set

Published on 14 Dec 2019 - 20:00

299

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Continuity requirements for Lebesgue-Stieltjes measure (Question 114X(b) in D.H. Fremlin)

Published on 12 Apr 2026 - 2:21

27

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What does $\forall x\in X,\forall \delta>0 E\cap B(x,\delta)\ne\emptyset$ imply for $E\subset X$

Published on 15 Dec 2019 - 14:16

1.2k

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Why this definition for Lebesgue measurable functions?

Published on 12 Apr 2026 - 4:54

List Question

Mode of convergence & DCT

Let $\alpha \in (0,1)$. Find a Borel subset $E$ of $[-1,1]$ s.t. $\lim_{r\to 0^{+}} \frac{m(E\cap [-r,r])}{2r}=\alpha.$

Proving the Lebesgue measure space completes the Borel measure space

Measure Theoretic rigorous formulation/definition of the Expectation Maximization algorithm (EM Algorithm)

Sard's Theorem with whatever function

Prove that there exists no Lebesgue-measurable set $A$ such that for every interval $I$ the Lebesgue measure of $A\cap I$ is half the length of $I$.

A variation of Borel-Cantelli Lemma 2

I want to raise a question about the notation of Dini derivatives

$g_n(x)=f(x+1/n)$ converges to $f$ in $L^1(\mathbb{R}$

Example of non measurable function in $\mathbb R^2$

Open intervals as union of closed intervals

Measures of subsets of a measurable set

Continuity requirements for Lebesgue-Stieltjes measure (Question 114X(b) in D.H. Fremlin)

What does $\forall x\in X,\forall \delta>0 E\cap B(x,\delta)\ne\emptyset$ imply for $E\subset X$

Why this definition for Lebesgue measurable functions?

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