List questions from measurable-sets

Published on 24 Mar 2020 - 20:31

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Given $U\subseteq\mathbb{C}$ an open set and $f : X\rightarrow \mathbb{C}$ measurable then $f^{-1}(U)$ is measurable

Published on 24 Feb 2026 - 7:06

283

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Proving that set $Z = \{(x,y) : F (x, y) = 0\}$ has measure $0$

Published on 13 May 2020 - 13:06

127

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Any example of measurable spaces where the measurable rectangles form an algebra on the product space?

Published on 14 May 2020 - 12:10

67

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Fremlin Question 132Xh

Published on 16 May 2020 - 16:54

133

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Generating the terminal $\sigma$-algebra

Published on 19 May 2020 - 18:40

29

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Prove that the set is measurable

Published on 20 May 2020 - 12:45

63

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Prove that $\text{sup}\{m(A\cap I)/m(I) : I \text{ open interval} \} = 1$

Published on 21 May 2020 - 8:02

110

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How to prove continuity of $f(x)=m(A\cap (-\infty ,x])$

Published on 21 May 2020 - 9:29

775

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Borel sigma algebra of extended Real Line

Published on 23 May 2020 - 8:02

301

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Measurable functions : $f(A) \in \mathcal{B}$

Published on 24 May 2020 - 18:21

478

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Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$

Published on 25 May 2020 - 9:08

97

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Could a limiting result (in terms of convergence) imply an equivalence relation?

Published on 25 May 2020 - 16:05

54

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Why sets of nonzero measure contain almost all the point from Borel-cantelli Leems?

Published on 02 Jun 2020 - 14:52

785

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Prove $f^{-1}(A)$ is measurable if A is measurable and $0<m \leq f'(x)\leq M <\infty$ on $\mathbb{R}$.

Published on 03 Jun 2020 - 19:47

List Question

Consider a measure space $(X,\mathcal{M},\mu$).

Given $U\subseteq\mathbb{C}$ an open set and $f : X\rightarrow \mathbb{C}$ measurable then $f^{-1}(U)$ is measurable

Proving that set $Z = \{(x,y) : F (x, y) = 0\}$ has measure $0$

Any example of measurable spaces where the measurable rectangles form an algebra on the product space?

Fremlin Question 132Xh

Generating the terminal $\sigma$-algebra

Prove that the set is measurable

Prove that $\text{sup}\{m(A\cap I)/m(I) : I \text{ open interval} \} = 1$

How to prove continuity of $f(x)=m(A\cap (-\infty ,x])$

Borel sigma algebra of extended Real Line

Measurable functions : $f(A) \in \mathcal{B}$

Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$

Could a limiting result (in terms of convergence) imply an equivalence relation?

Why sets of nonzero measure contain almost all the point from Borel-cantelli Leems?

Prove $f^{-1}(A)$ is measurable if A is measurable and $0<m \leq f'(x)\leq M <\infty$ on $\mathbb{R}$.

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