List questions from measurable-functions

Published on 20 May 2020 - 18:11

169

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$E$ is finite measurable set, if $f_n$ converges in measure to $f$ then $\dfrac{1}{f_n}$ converges in measure to $\dfrac{1}{f}$

Published on 21 May 2020 - 17:33

776

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Borel sigma algebra of extended Real Line

Published on 25 Mar 2026 - 8:09

181

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Density of a image measure

Published on 24 May 2020 - 16:35

302

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

Published on 25 Mar 2026 - 8:08

479

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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 Mar 2026 - 8:10

45

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Is there a missing condition in this statement regarding Borel measurability

Published on 28 Mar 2026 - 20:53

24

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Convergence in measure and related inequality

Published on 29 May 2020 - 8:39

836

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Radon-Nikodym derivative for discrete measures

Published on 29 May 2020 - 15:21

423

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Discrete measure and Lebesgue measurability

Published on 29 May 2020 - 16:15

402

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For measurable $f: \mathbb{R} \rightarrow \mathbb{R}$ prove $f(x)$ and $\frac{1}{f(1/x)}$ cannot both be Lebesgue integrable.

Published on 30 May 2020 - 19:23

140

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Show that $f$ is measurable if $f\lvert f \rvert^{p-1}$ is measurable

Published on 31 May 2020 - 8:07

905

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Simple function is measurable

Published on 01 Jun 2020 - 4:28

77

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Prove that $(\mu_1 \otimes \mu_2)\circ {\Pi_1}^{-1}=\mu_1$

Published on 27 Mar 2026 - 14:52

112

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Composition of continuous and nonmeasurable function is measurable.

Published on 27 Mar 2026 - 6:09

List Question

Definition of $\mathcal{F}$-scalarly measurable.

$E$ is finite measurable set, if $f_n$ converges in measure to $f$ then $\dfrac{1}{f_n}$ converges in measure to $\dfrac{1}{f}$

Borel sigma algebra of extended Real Line

Density of a image measure

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

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

Is there a missing condition in this statement regarding Borel measurability

Convergence in measure and related inequality

Radon-Nikodym derivative for discrete measures

Discrete measure and Lebesgue measurability

For measurable $f: \mathbb{R} \rightarrow \mathbb{R}$ prove $f(x)$ and $\frac{1}{f(1/x)}$ cannot both be Lebesgue integrable.

Show that $f$ is measurable if $f\lvert f \rvert^{p-1}$ is measurable

Simple function is measurable

Prove that $(\mu_1 \otimes \mu_2)\circ {\Pi_1}^{-1}=\mu_1$

Composition of continuous and nonmeasurable function is measurable.

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