Question

Definition of a measurable function with respect to $\sigma$ - algebra

score 42 · Answer 1 · 2024-03-06 17:51:42

Definition of a measurable function with respect to $\sigma$ - algebra

Published on 06 Mar 2024 - 17:51

score 46 · Answer 2 · 2024-03-09 23:20:19

Show the existence of a sequence of simple functions such that $\lim_{n\to\infty}\varphi_n(x)=f(x)$ and $\Vert\varphi _n(x)\Vert\leq\Vert f(x)\Vert$

score 77 · Answer 3 · 2026-03-26 09:16:25

77

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Is the median a measurable function of the probability distribution?

Published on 26 Mar 2026 - 9:16

score 91 · Answer 4 · 2024-03-11 13:05:19

91

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Show that the measure $\mu ([a,b]) = \ln \left( \frac{1+b}{1+a} \right)$ is invariant for function $\Phi_k$.

Published on 11 Mar 2024 - 13:05

score 38 · Answer 5 · 2024-03-13 11:08:52

38

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Measurability of an integral operator?!

Published on 13 Mar 2024 - 11:08

score 18 · Answer 6 · 2026-03-27 19:42:29

18

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Random measure and empirical spectral distribution

Published on 27 Mar 2026 - 19:42

score 46 · Answer 7 · 2026-03-26 16:09:50

46

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Composition of Lebesgue measurable function and Invertible linear transformation is Lebesgue measurable

Published on 26 Mar 2026 - 16:09

score 287 · Answer 8 · 2026-03-08 09:38:17

287

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Lebesgue integral of a measurable function squeezed between two integrable functions

Published on 08 Mar 2026 - 9:38

score 57 · Answer 9 · 2016-03-01 21:16:43

57

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Measurable functions : Is X F Measurable?

Published on 01 Mar 2016 - 21:16

score 88 · Answer 10 · 2014-01-07 14:45:50

88

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Question about integrable functions and integrands

Published on 07 Jan 2014 - 14:45

score 3k · Answer 11 · 2026-03-29 15:54:37

3k

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Show that if $E\subset\mathbb{R}$ is a measurable set, so $f:E\rightarrow \mathbb{R}$ is a measurable function.

Published on 29 Mar 2026 - 15:54

score 23.2k · Answer 12 · 2014-03-02 12:14:50

23.2k

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$f$ a real, continuous function, is it measurable?

Published on 02 Mar 2014 - 12:14

score 178 · Answer 13 · 2017-04-18 03:01:35

178

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Sequence of measurable functions $\{g_n\}_{n=1}^{\infty}$ such that $\lim_{n\to\infty}\int_{0}^{1}f(t)g_n(t)dt=\int_0^1f(t)dt$ whenever $f\in C[0,1]$

Published on 18 Apr 2017 - 3:01

score 1.1k · Answer 14 · 2017-04-18 16:06:47

1.1k

Views

Counter example that Egoroff's Theorem does not hold for infinite measure domain

Published on 18 Apr 2017 - 16:06

score 198 · Answer 15 · 2017-04-20 15:27:26

198

Views

Polish space of measurable functions

Published on 20 Apr 2017 - 15:27

List Question

Definition of a measurable function with respect to $\sigma$ - algebra

Show the existence of a sequence of simple functions such that $\lim_{n\to\infty}\varphi_n(x)=f(x)$ and $\Vert\varphi _n(x)\Vert\leq\Vert f(x)\Vert$

Is the median a measurable function of the probability distribution?

Show that the measure $\mu ([a,b]) = \ln \left( \frac{1+b}{1+a} \right)$ is invariant for function $\Phi_k$.

Measurability of an integral operator?!

Random measure and empirical spectral distribution

Composition of Lebesgue measurable function and Invertible linear transformation is Lebesgue measurable

Lebesgue integral of a measurable function squeezed between two integrable functions

Measurable functions : Is X F Measurable?

Question about integrable functions and integrands

Show that if $E\subset\mathbb{R}$ is a measurable set, so $f:E\rightarrow \mathbb{R}$ is a measurable function.

$f$ a real, continuous function, is it measurable?

Sequence of measurable functions $\{g_n\}_{n=1}^{\infty}$ such that $\lim_{n\to\infty}\int_{0}^{1}f(t)g_n(t)dt=\int_0^1f(t)dt$ whenever $f\in C[0,1]$

Counter example that Egoroff's Theorem does not hold for infinite measure domain

Polish space of measurable functions

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