List questions from measure-theory

Published on 15 May 2026 - 8:15

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Does $\{A\subset Y\mid f^{-1}(A)\in \mathcal F\}=\{A\in \mathcal W\mid f^{-1}(A)\in \mathcal F\}$?

Published on 14 Apr 2026 - 2:05

153

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Limit of probability Radon measures for balls

Published on 12 Apr 2026 - 22:47

181

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If $\Omega$ has finite measure and $f \in L^p(\Omega)$ then for $1 \leq q \leq p$ we have $f \in L^q(\Omega)$ and the following estimate.

Published on 16 May 2026 - 20:52

49

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An inequality about borel measures in a proof

Published on 05 May 2026 - 17:09

91

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How to Modify a Borel function in a Borel way-Self study

Published on 10 May 2026 - 18:13

126

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Constructing a weird probability measure

Published on 11 Apr 2026 - 17:08

351

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Smallest Sigma Field Generated by Maps

Published on 14 Apr 2026 - 18:55

230

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Why Koopman operator is defined on $L^\infty$ space?

Published on 13 Apr 2026 - 2:50

132

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No continuous function $f$ on $\mathbb{R}$ such that $f(x)=1_{[0,1]}(x)$ almost everywhere

Published on 16 May 2026 - 20:54

72

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Does there exist an open subset $A \subset [0,1]$ such that $m_(A)\neq m_(\bar{A})$?

Published on 16 May 2026 - 20:53

769

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Proof that continuous curve in $\mathbb{R}^2$ has Lebesgue measure zero

Published on 16 May 2026 - 20:52

924

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Show $B(t)/t\to0$ a.s. for $t\to\infty$ where $B(t)$ is SBM

Published on 13 Apr 2026 - 15:24

1.1k

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Exercise 36 Ch 1 in Stein's Real Analysis

Published on 16 May 2026 - 20:55

156

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An enumeration of rational s.t. $\bigcup_{n=1}^\infty \left(r_n-\frac{1}{n},r_n+\frac{1}{n}\right)\neq \mathbb R$, is it possible?

Published on 14 Apr 2026 - 5:15

List Question

Convolution square of the Cantor set

Does $\{A\subset Y\mid f^{-1}(A)\in \mathcal F\}=\{A\in \mathcal W\mid f^{-1}(A)\in \mathcal F\}$?

Limit of probability Radon measures for balls

If $\Omega$ has finite measure and $f \in L^p(\Omega)$ then for $1 \leq q \leq p$ we have $f \in L^q(\Omega)$ and the following estimate.

An inequality about borel measures in a proof

How to Modify a Borel function in a Borel way-Self study

Constructing a weird probability measure

Smallest Sigma Field Generated by Maps

Why Koopman operator is defined on $L^\infty$ space?

No continuous function $f$ on $\mathbb{R}$ such that $f(x)=1_{[0,1]}(x)$ almost everywhere

Does there exist an open subset $A \subset [0,1]$ such that $m_(A)\neq m_(\bar{A})$?

Proof that continuous curve in $\mathbb{R}^2$ has Lebesgue measure zero

Show $B(t)/t\to0$ a.s. for $t\to\infty$ where $B(t)$ is SBM

Exercise 36 Ch 1 in Stein's Real Analysis

An enumeration of rational s.t. $\bigcup_{n=1}^\infty \left(r_n-\frac{1}{n},r_n+\frac{1}{n}\right)\neq \mathbb R$, is it possible?

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