List questions from measure-theory

Published on 14 Apr 2026 - 4:00

603

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If $A \times B$ is Lebesgue measurable in $\mathbb{R}^2$ and $B$ is Lebesgue measurable in $\mathbb{R}$ then $A$ is so?

Published on 15 Apr 2026 - 6:01

101

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Random variables $X,Y$ such that $E(X|Y)=E(Y|X)$ a.s.

Published on 15 Apr 2026 - 9:48

113

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integrable random variables $X,Y$ such that $E(X|Y)=X$ a.s. and $E(Y|X)=Y$ a.s.

Published on 15 Apr 2026 - 8:28

95

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Show $\lim_{a \to 0} a \cdot \mu (\{ x \in \mathbb{R} : |f(x)| > a \}) = 0$ for $f \in L^1 (\mathbb{R})$, $a>0$

Published on 16 Apr 2026 - 3:06

673

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Recurrent Markov chain has an invariant measure

Published on 11 May 2026 - 8:56

38

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On the existence of a particular type of finite measure on $\mathbb N$

Published on 14 Apr 2026 - 11:40

494

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weak* convergence of convolution between mollifiers and Radon measure

Published on 25 Mar 2026 - 11:01

67

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Prove that a set of norm p is of measure zero

Published on 15 Apr 2026 - 5:24

63

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If $|\langle f, g \rangle| = \| f \|_2 \|g\|_2$ then $\exists \alpha, \beta \in \mathbb{R} $ s.t. $\alpha f = \beta g $

Published on 16 Apr 2026 - 20:24

70

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Bochner integrability of mappings of Bochner integrable functions

Published on 11 Apr 2026 - 0:30

92

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Showing equivalence in a complex measure space

Published on 10 May 2026 - 15:22

75

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Complete Measure spaces

Published on 10 May 2026 - 21:14

161

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Measures on the Sigma Algebra generated by a set

Published on 13 Apr 2026 - 23:45

2.2k

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Intuition Wanted: Why Define Integrals Component-Wise

Published on 14 May 2026 - 18:29

List Question

Proving DCT from Fatou's Lemma

If $A \times B$ is Lebesgue measurable in $\mathbb{R}^2$ and $B$ is Lebesgue measurable in $\mathbb{R}$ then $A$ is so?

Random variables $X,Y$ such that $E(X|Y)=E(Y|X)$ a.s.

integrable random variables $X,Y$ such that $E(X|Y)=X$ a.s. and $E(Y|X)=Y$ a.s.

Show $\lim_{a \to 0} a \cdot \mu (\{ x \in \mathbb{R} : |f(x)| > a \}) = 0$ for $f \in L^1 (\mathbb{R})$, $a>0$

Recurrent Markov chain has an invariant measure

On the existence of a particular type of finite measure on $\mathbb N$

weak* convergence of convolution between mollifiers and Radon measure

Prove that a set of norm p is of measure zero

If $|\langle f, g \rangle| = \| f \|_2 \|g\|_2$ then $\exists \alpha, \beta \in \mathbb{R} $ s.t. $\alpha f = \beta g $

Bochner integrability of mappings of Bochner integrable functions

Showing equivalence in a complex measure space

Complete Measure spaces

Measures on the Sigma Algebra generated by a set

Intuition Wanted: Why Define Integrals Component-Wise

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