List questions from measurable-functions

Published on 26 Jul 2019 - 18:07

60

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Understanding a step in a proof of $\lim_{n\to\infty}\int_{[0,n]}(1+\frac{x}{n})^ne^{-2x}dx$

Published on 27 Jul 2019 - 6:59

116

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Integrability in Definition of Subharmonic functions

Published on 27 Jul 2019 - 12:06

72

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$|\{ |f| > t \}| \leq Ct^{-2} \implies \int_{E}|f| \leq D\sqrt{|E|}$

Published on 02 Aug 2019 - 1:37

355

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Measurable functions with arbitrarily small periods are constant

Published on 10 Aug 2019 - 7:44

80

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A question on convergence to zero of measurable sets

Published on 13 Aug 2019 - 11:41

166

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Sequence using Fatou's lemma

Published on 17 Aug 2019 - 12:11

205

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measureability of a function and its relation to the completion of the measure

Published on 22 Aug 2019 - 3:14

304

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Lusin's Theorem: Theorem 2.24 from Rudin RCA

Published on 27 Aug 2019 - 20:05

29

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On proving a space to be measurable space and finding topology generated by it.

Published on 02 Sep 2019 - 16:55

155

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If $f(\cdot, \cdot)$ is measurable in each variable and $g(\cdot)$ is measurable, then $x \mapsto f(x,g(x))$ is measurable?

Published on 05 Sep 2019 - 9:03

81

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Is $g(x, f(x))$ measurable if $f$ and $g$ are?

Published on 07 Sep 2019 - 4:28

37

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Is this proof of measurability correct?

Published on 07 Sep 2019 - 23:31

1.3k

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Use the fact that a lower semi-continuous function is Borel measurable to conclude every continuous function is Borel measurable

Published on 25 Mar 2026 - 7:42

146

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Help showing that $g(x)$ is differentiable.

Published on 13 Sep 2019 - 22:16

List Question

Relationship between the different definitions of measurable functions

Understanding a step in a proof of $\lim_{n\to\infty}\int_{[0,n]}(1+\frac{x}{n})^ne^{-2x}dx$

Integrability in Definition of Subharmonic functions

$|\{ |f| > t \}| \leq Ct^{-2} \implies \int_{E}|f| \leq D\sqrt{|E|}$

Measurable functions with arbitrarily small periods are constant

A question on convergence to zero of measurable sets

Sequence using Fatou's lemma

measureability of a function and its relation to the completion of the measure

Lusin's Theorem: Theorem 2.24 from Rudin RCA

On proving a space to be measurable space and finding topology generated by it.

If $f(\cdot, \cdot)$ is measurable in each variable and $g(\cdot)$ is measurable, then $x \mapsto f(x,g(x))$ is measurable?

Is $g(x, f(x))$ measurable if $f$ and $g$ are?

Is this proof of measurability correct?

Use the fact that a lower semi-continuous function is Borel measurable to conclude every continuous function is Borel measurable

Help showing that $g(x)$ is differentiable.

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