Question

Different notions of measurability lead to strikingly different (if not opposite) conclusions

score 69 · Answer 1 · 2022-08-07 16:36:52

69

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Different notions of measurability lead to strikingly different (if not opposite) conclusions

Published on 07 Aug 2022 - 16:36

score 49 · Answer 2 · 2022-08-08 02:31:44

49

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Let $f,g \in E^X$ such that $f$ is $\mu$-measurable and $f=g$ $\mu$-a.e. Then $g$ is $\mu$-measurable

Published on 08 Aug 2022 - 2:31

score 83 · Answer 3 · 2022-08-08 17:42:12

Non-complete measure spaces: approximate a $[0, \infty]$-valued $\mu$-measurable function by an increasing sequence of $\mu$-simple functions

score 140 · Answer 4 · 2026-03-26 22:57:47

140

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How does professor Amann conclude that "Corollary 1.5 remains true for incomplete measure spaces"?

Published on 26 Mar 2026 - 22:57

score 71 · Answer 5 · 2022-08-10 15:00:34

71

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Let $\varphi_n, \psi$ be simple functions such that $(\varphi_n)$ is increasing and $\psi\le\lim_n\varphi_n$. Then $\int\psi\le\lim_n \int \varphi_n$

Published on 10 Aug 2022 - 15:00

score 186 · Answer 6 · 2026-03-26 04:29:04

186

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How to compute Push Forward Measures?

Published on 26 Mar 2026 - 4:29

score 67 · Answer 7 · 2026-02-23 15:16:36

67

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Can we say that $|\operatorname{supp}u\cap \{u=0\}|=0$?

Published on 23 Feb 2026 - 15:16

score 59 · Answer 8 · 2022-08-12 23:07:00

59

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What does a $\mathcal A$-measurable function mean?

Published on 12 Aug 2022 - 23:07

score 191 · Answer 9 · 2026-03-30 05:24:57

191

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Prove or disprove that $u=0$ a.e. on $\Bbb R^d$

Published on 30 Mar 2026 - 5:24

score 62 · Answer 10 · 2022-08-20 18:52:14

62

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One-to-one correspondence between measures and linear functionals satisfying the MCP

Published on 20 Aug 2022 - 18:52

score 33 · Answer 11 · 2022-08-22 16:36:49

33

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If $E$ is countable and $\mathcal{E} = 2^{E}$, then every numerical function on $E$ is $\mathcal{E}$-measurable

Published on 22 Aug 2022 - 16:36

score 64 · Answer 12 · 2022-08-27 10:49:25

64

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(Egorov type) Convergence of solutions of heat equation to their initial condition as $t\to 0^+$ when the initial condition is in $L^2$

Published on 27 Aug 2022 - 10:49

score 32 · Answer 13 · 2022-09-03 14:15:17

32

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Range = Codomain for a measurable map?

Published on 03 Sep 2022 - 14:15

score 39 · Answer 14 · 2026-03-26 14:19:23

39

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How can I prove that these two statements relating to a measurable function are equivalent?

Published on 26 Mar 2026 - 14:19

score 172 · Answer 15 · 2026-03-26 22:57:55

172

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Motivation behind the definition of measurable functions.

Published on 26 Mar 2026 - 22:57

List Question

Different notions of measurability lead to strikingly different (if not opposite) conclusions

Let $f,g \in E^X$ such that $f$ is $\mu$-measurable and $f=g$ $\mu$-a.e. Then $g$ is $\mu$-measurable

Non-complete measure spaces: approximate a $[0, \infty]$-valued $\mu$-measurable function by an increasing sequence of $\mu$-simple functions

How does professor Amann conclude that "Corollary 1.5 remains true for incomplete measure spaces"?

Let $\varphi_n, \psi$ be simple functions such that $(\varphi_n)$ is increasing and $\psi\le\lim_n\varphi_n$. Then $\int\psi\le\lim_n \int \varphi_n$

How to compute Push Forward Measures?

Can we say that $|\operatorname{supp}u\cap \{u=0\}|=0$?

What does a $\mathcal A$-measurable function mean?

Prove or disprove that $u=0$ a.e. on $\Bbb R^d$

One-to-one correspondence between measures and linear functionals satisfying the MCP

If $E$ is countable and $\mathcal{E} = 2^{E}$, then every numerical function on $E$ is $\mathcal{E}$-measurable

(Egorov type) Convergence of solutions of heat equation to their initial condition as $t\to 0^+$ when the initial condition is in $L^2$

Range = Codomain for a measurable map?

How can I prove that these two statements relating to a measurable function are equivalent?

Motivation behind the definition of measurable functions.

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