List questions from measurable-functions

Published on 07 Jun 2019 - 22:44

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Definition de $L^1((0,T);W^{1,\infty}(\mathbb R))$.

Published on 25 Mar 2026 - 17:45

19

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Measurablity of single maps from measurability of a composition

Published on 25 Mar 2026 - 3:21

404

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Prove that $\int_If\phi dm=\int_Ig\phi dm$ implies $f=g$ a.e over $I$

Published on 22 Jun 2019 - 1:55

1.1k

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Given $f$ integrable and $\int_E f\geq 0$ for every $E$ measurable set prove $f(x)\geq 0$ almost everywhere.

Published on 25 Jun 2019 - 4:19

146

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Question: Let $f$ is continuous, $g$ is measurable function.Show that composition function $f\circ g$ is measurable

Published on 28 Jun 2019 - 8:09

53

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Measurable (epsilon-optimal) selection for universally measurable functions

Published on 04 Jul 2019 - 4:46

144

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Absolutely continuous function vanishes on a set, does its derivative vanish?

Published on 23 Feb 2026 - 4:52

34

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Filtration infinitesimal glance into the future

Published on 10 Jul 2019 - 21:10

125

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Sequences of step functions and measurable functions

Published on 23 Feb 2026 - 7:52

995

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Prove the inverse of a lebesgue measurable function is measurable

Published on 14 Jul 2019 - 6:53

44

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Relation between progressive measurable processes and stopping times

Published on 15 Jul 2019 - 21:53

313

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Uniqueness of Lebesgue measure

Published on 21 Jul 2019 - 17:12

72

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Proving that the sequence $φ_n:=\frac 1 n \sum_{k=0} ^{n^2} kχ_{E_{n,k}}$ is monotone

Published on 24 Jul 2019 - 1:44

51

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Measurability of probability densities as maps from a parameter space

Published on 24 Jul 2019 - 8:10

List Question

If $\int_0^1f^k(x)\;dx\le M$, then $m(\{x\in[0,1]:f(x)>1\})=0$.

Definition de $L^1((0,T);W^{1,\infty}(\mathbb R))$.

Measurablity of single maps from measurability of a composition

Prove that $\int_If\phi dm=\int_Ig\phi dm$ implies $f=g$ a.e over $I$

Given $f$ integrable and $\int_E f\geq 0$ for every $E$ measurable set prove $f(x)\geq 0$ almost everywhere.

Question: Let $f$ is continuous, $g$ is measurable function.Show that composition function $f\circ g$ is measurable

Measurable (epsilon-optimal) selection for universally measurable functions

Absolutely continuous function vanishes on a set, does its derivative vanish?

Filtration infinitesimal glance into the future

Sequences of step functions and measurable functions

Prove the inverse of a lebesgue measurable function is measurable

Relation between progressive measurable processes and stopping times

Uniqueness of Lebesgue measure

Proving that the sequence $φ_n:=\frac 1 n \sum_{k=0} ^{n^2} kχ_{E_{n,k}}$ is monotone

Measurability of probability densities as maps from a parameter space

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