Question

$g \in L^p_{\operatorname{loc}}(\Omega) \Longleftrightarrow |g|^p \, \chi_\Omega \in L^1_{\operatorname{loc}}(\mathbb R^n) ? $

score 53 · Answer 1 · 2026-04-17 08:00:57

53

Views

$g \in L^p_{\operatorname{loc}}(\Omega) \Longleftrightarrow |g|^p \, \chi_\Omega \in L^1_{\operatorname{loc}}(\mathbb R^n) ? $

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score 29 · Answer 2 · 2026-04-14 14:53:53

29

Views

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score 48 · Answer 3 · 2026-04-14 14:55:48

48

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score 21 · Answer 5 · 2026-04-13 04:07:14

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score 71 · Answer 6 · 2026-04-12 00:24:57

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score 35 · Answer 7 · 2026-04-14 09:28:44

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score 26 · Answer 8 · 2026-04-14 04:10:02

26

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score 22 · Answer 9 · 2026-03-25 23:13:08

22

Views

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score 31 · Answer 12 · 2026-04-10 05:17:13

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score 26 · Answer 13 · 2026-04-15 22:13:11

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29

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score 17 · Answer 15 · 2026-04-11 13:32:46

17

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List Question

$g \in L^p_{\operatorname{loc}}(\Omega) \Longleftrightarrow |g|^p \, \chi_\Omega \in L^1_{\operatorname{loc}}(\mathbb R^n) ? $

Riesz–Markov–Kakutani representation theorem on a $\sigma$-compact space

Tonelli and standard procedure application for h = f(x-y)g(x)

Measurability of the set of elements who belong to a infinite amount of subsets in a sequence

Proof of this subaditivity-related measure-theory inequality

Is the set A measurable?

Bijection and outer measure of two sets

Show that $\mu$ is the Lebesgue measure on $\mathbb{R}$, $\mu$ being invariant by translation and $\mu(]0,1])=1$

An integral of a Borel measurable function w.r.t. Borel measure and that w.r.t. Lebesgue measure coincide with each other?

Is there a framework where a derivative of a singular function makes sense?

Show that if $f$ is right continuous then $f$ is measurable

Fourier Transforms and changing measures

How to pick a measurable set $U$ s.t. $\mathcal N^c \subseteq U\subseteq I $ and $m_*(U)<1-\varepsilon, \forall\epsilon\gt 0$

Distribution theory of finite sum

Boundary of Ahlfors n-dimensional domain measures 0

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