List questions from measurable-functions

Published on 05 Nov 2019 - 20:24

256

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Proving a vector space contains all Borel-measurable functions

Published on 09 Mar 2026 - 5:52

219

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Every monotonic function $f:\mathbb{R} \rightarrow \mathbb{R}$ is measurable

Published on 10 Nov 2019 - 14:49

521

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Measurable function raised to a power still a measurable funktion?

Published on 12 Nov 2019 - 15:19

47

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Consistent family of measures and Bochner Theorem

Published on 13 Nov 2019 - 22:52

116

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$\int_\mathbb{R}\psi(t)f(t)dt=0$ for all Lebesgue integrable functions $f$ with $\int_\mathbb{R}f(t)dt=0$ implies $\psi$ is constant

Published on 14 Nov 2019 - 17:42

33

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If $f$ is measured then for every real number a set {$x: f (x) = a$} measured, is the opposite true?

Published on 14 Nov 2019 - 22:54

36

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If $f:\mathbb{R}\to\mathbb{R}$ measurable with $f(x) \neq 0$, prove there exists measurable $g(x)$ with $\frac{1}{2}f(x) < g(x) < f(x)$

Published on 16 Nov 2019 - 15:42

193

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Measurable function with parameters

Published on 25 Mar 2026 - 12:12

107

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Show that an $\mathcal{A}$-integrable function is $\mu$-integrable

Published on 18 Nov 2019 - 12:57

87

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What can we say about continuity by knowing Borel-Measurability?

Published on 21 Nov 2019 - 12:53

84

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Proving that the set of continuous real functions is dense in the norm $L_{1}$ in the set of integrable functions

Published on 26 Mar 2026 - 0:53

62

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Prove that the following set has full measure (i.e. has probability one):

Published on 22 Nov 2019 - 18:38

126

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Set of measurable function on a Hilbert space

Published on 25 Mar 2026 - 6:26

86

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The number of jumps in a continuous time markov chain is a random variable.

Published on 26 Nov 2019 - 11:53

List Question

Limit of a sequence of indicators function.

Proving a vector space contains all Borel-measurable functions

Every monotonic function $f:\mathbb{R} \rightarrow \mathbb{R}$ is measurable

Measurable function raised to a power still a measurable funktion?

Consistent family of measures and Bochner Theorem

$\int_\mathbb{R}\psi(t)f(t)dt=0$ for all Lebesgue integrable functions $f$ with $\int_\mathbb{R}f(t)dt=0$ implies $\psi$ is constant

If $f$ is measured then for every real number a set {$x: f (x) = a$} measured, is the opposite true?

If $f:\mathbb{R}\to\mathbb{R}$ measurable with $f(x) \neq 0$, prove there exists measurable $g(x)$ with $\frac{1}{2}f(x) < g(x) < f(x)$

Measurable function with parameters

Show that an $\mathcal{A}$-integrable function is $\mu$-integrable

What can we say about continuity by knowing Borel-Measurability?

Proving that the set of continuous real functions is dense in the norm $L_{1}$ in the set of integrable functions

Prove that the following set has full measure (i.e. has probability one):

Set of measurable function on a Hilbert space

The number of jumps in a continuous time markov chain is a random variable.

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