List questions from measure-theory

Published on 12 Apr 2026 - 7:57

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Every finite measure on a metric space is regular

Published on 12 Apr 2026 - 9:59

355

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Is a simply connected subset of $\mathbb{R}^n$ necessarily measurable?

Published on 12 Apr 2026 - 3:20

332

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Constructing sigma algebras in countably many steps

Published on 10 May 2026 - 20:49

96

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Question about Coupling of Measures

Published on 14 May 2026 - 18:52

940

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Young's convolution inequality: Equivalent representations

Published on 10 May 2026 - 22:47

201

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Definition of "almost everywhere"

Published on 09 Apr 2026 - 18:21

193

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Rewrite $ \int_{\{(a,b,c)\in \mathbb{R}^3\text{ s.t. } a=b+c\}}dP_{X,Y,Z}=1 $ as conditions on boxes in $\mathbb{R}^3$

Published on 16 Apr 2026 - 0:58

84

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Inclusion relationship between $\mathscr l^p$ spaces

Published on 08 Apr 2026 - 21:43

31

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How to prove that $L(I)=m(I \setminus A)+m(A)$?

Published on 12 Apr 2026 - 1:34

138

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Exchange limit on bounds of Lebesgue integral

Published on 10 Apr 2026 - 12:29

73

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Help in understanding the proof of a claim made in the proof of the Beppi Levi Theorem in Schilling.

Published on 10 Apr 2026 - 17:11

329

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If $\mu$ has a density with respect to the Lebesgue measure, is $C_c(\mathbb R)$ dense in $L^p(\mu)$?

Published on 13 Apr 2026 - 21:18

82

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Is the Jacobian different for different $l^p$ norms?

Published on 12 Apr 2026 - 5:35

39

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An example $\limsup \mu_n(F)<\mu(F)$

Published on 29 Apr 2026 - 1:40

List Question

Existence of a Certain Transport Map

Every finite measure on a metric space is regular

Is a simply connected subset of $\mathbb{R}^n$ necessarily measurable?

Constructing sigma algebras in countably many steps

Question about Coupling of Measures

Young's convolution inequality: Equivalent representations

Definition of "almost everywhere"

Rewrite $ \int_{\{(a,b,c)\in \mathbb{R}^3\text{ s.t. } a=b+c\}}dP_{X,Y,Z}=1 $ as conditions on boxes in $\mathbb{R}^3$

Inclusion relationship between $\mathscr l^p$ spaces

How to prove that $L(I)=m(I \setminus A)+m(A)$?

Exchange limit on bounds of Lebesgue integral

Help in understanding the proof of a claim made in the proof of the Beppi Levi Theorem in Schilling.

If $\mu$ has a density with respect to the Lebesgue measure, is $C_c(\mathbb R)$ dense in $L^p(\mu)$?

Is the Jacobian different for different $l^p$ norms?

An example $\limsup \mu_n(F)<\mu(F)$

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