Question

Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

score 191 · Answer 1 · 2026-04-13 22:38:28

Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

Published on 13 Apr 2026 - 22:38

score 124 · Answer 2 · 2026-04-15 13:22:43

$E\subset\mathbb{R}^n$ is measurable $\Leftrightarrow$ $\exists$ a sequence of measurable subsets $\{E_k\}_{k\geq1}$ s.t. $m(E_k)\to m^*(E)$.

score 122 · Answer 3 · 2026-04-08 21:58:50

122

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Convergence in measure, a few questions.

Published on 08 Apr 2026 - 21:58

score 181 · Answer 4 · 2026-04-12 04:36:01

181

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Proposition 4 of Chapter $4$ From Royden Real Analysis

Published on 12 Apr 2026 - 4:36

score 667 · Answer 5 · 2026-04-14 14:52:05

667

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Lebesgue integral of f(x) over R is equal to Lebesgue integral of f(x+t) over R

Published on 14 Apr 2026 - 14:52

score 38 · Answer 6 · 2026-04-15 13:07:57

38

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Questions about null sets

Published on 15 Apr 2026 - 13:07

score 146 · Answer 7 · 2026-04-15 13:14:45

146

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Is $(x,x)$ where $x\in A\subset \mathbb{R}$ measurable?

Published on 15 Apr 2026 - 13:14

score 615 · Answer 8 · 2026-04-15 13:22:52

615

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Show that $f^{2}$ is measurable on the interval I

Published on 15 Apr 2026 - 13:22

score 403 · Answer 9 · 2026-04-15 13:13:51

403

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Is the set $[0,\infty]$ Lebesgue Measurable?

Published on 15 Apr 2026 - 13:13

score 509 · Answer 10 · 2026-04-15 13:17:52

509

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Lebesgue measurability of a function with finite points of discontinuity

Published on 15 Apr 2026 - 13:17

score 31 · Answer 11 · 2026-03-26 17:53:35

31

Views

Check consistency and extend, if possible, measures of union and intersection of four sets of quantum-information-theoretic interest

Published on 26 Mar 2026 - 17:53

score 41 · Answer 12 · 2026-04-05 23:28:29

41

Views

If $f_n \to f$ uniformly where $f_n$ are continuous then $\int_{0}^{1-\frac{1}{n}}f_n \to \int_{0}^{1}f$

Published on 05 Apr 2026 - 23:28

score 53 · Answer 13 · 2026-04-15 09:24:58

53

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Prove $\Lambda(f)=\int_{0}^{1}\frac{f(t)}{\sqrt{|x-t|}}dt$ is bounded operator from $L^2[0,1]$ to $L^2[0,1]$

Published on 15 Apr 2026 - 9:24

score 33 · Answer 14 · 2026-04-15 02:52:09

33

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Let $f \in L^1(X)$ where $\mu(X)<\infty$ then $g(t)=\int_X\cos(tf(x))dx$ is in $C^1(\mathbb{R})$

Published on 15 Apr 2026 - 2:52

score 37 · Answer 15 · 2026-04-15 13:18:59

37

Views

Thoughts on almost everywhere concept

Published on 15 Apr 2026 - 13:18

List Question

Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

$E\subset\mathbb{R}^n$ is measurable $\Leftrightarrow$ $\exists$ a sequence of measurable subsets $\{E_k\}_{k\geq1}$ s.t. $m(E_k)\to m^*(E)$.

Convergence in measure, a few questions.

Proposition 4 of Chapter $4$ From Royden Real Analysis

Lebesgue integral of f(x) over R is equal to Lebesgue integral of f(x+t) over R

Questions about null sets

Is $(x,x)$ where $x\in A\subset \mathbb{R}$ measurable?

Show that $f^{2}$ is measurable on the interval I

Is the set $[0,\infty]$ Lebesgue Measurable?

Lebesgue measurability of a function with finite points of discontinuity

Check consistency and extend, if possible, measures of union and intersection of four sets of quantum-information-theoretic interest

If $f_n \to f$ uniformly where $f_n$ are continuous then $\int_{0}^{1-\frac{1}{n}}f_n \to \int_{0}^{1}f$

Prove $\Lambda(f)=\int_{0}^{1}\frac{f(t)}{\sqrt{|x-t|}}dt$ is bounded operator from $L^2[0,1]$ to $L^2[0,1]$

Let $f \in L^1(X)$ where $\mu(X)<\infty$ then $g(t)=\int_X\cos(tf(x))dx$ is in $C^1(\mathbb{R})$

Thoughts on almost everywhere concept

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