Question

$L^p$ Approximation of a $L^p$ function on $\Bbb R$ for $1\leq p<\infty$

score 84 · Answer 1 · 2026-04-06 23:59:14

84

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$L^p$ Approximation of a $L^p$ function on $\Bbb R$ for $1\leq p<\infty$

Published on 06 Apr 2026 - 23:59

score 21 · Answer 2 · 2020-07-22 15:04:23

21

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Question regarding measure theory and Lebesgue integral

Published on 22 Jul 2020 - 15:04

score 41 · Answer 3 · 2020-07-23 00:58:19

41

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$f:[0,1]\rightarrow[0,1]$, measurable, and $\int_{[0,1]}f(x)dx=y\implies m\{x:f(x)>\frac{y}{2}\}\geq\frac{y}{2}$.

Published on 23 Jul 2020 - 0:58

score 311 · Answer 4 · 2026-04-07 00:02:09

311

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A question for a measurable function $g$ on a finite measure space such that $fg\in L^p$ for all $f\in L^p$

Published on 07 Apr 2026 - 0:02

score 69 · Answer 5 · 2020-07-23 14:56:56

69

Views

A question about measure theory.

Published on 23 Jul 2020 - 14:56

score 98 · Answer 6 · 2020-07-24 00:42:32

98

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Inequality concerning functions quadratic decay of distribution $m(|f|>\lambda)\leq C\lambda^{-2}$

Published on 24 Jul 2020 - 0:42

score 54 · Answer 7 · 2026-03-30 20:39:21

54

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Differentiating under the Integral with Carathéodory.

Published on 30 Mar 2026 - 20:39

score 36 · Answer 8 · 2020-07-24 14:51:25

36

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Rewrite $\int_{\mathbb{R^4}}\int_{\mathbb{R^4}}\ h(|x|^2,|y|^2,x\cdot y)\ dx\ dy$ as $\int\int\limits_{\Omega}\int\ J(u,v,w)\ h(u,v,w)\ du\ dv\ dw$.

Published on 24 Jul 2020 - 14:51

score 85 · Answer 9 · 2026-03-30 20:42:42

85

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Explain how to translate Lebesgue to Riemann integral in expected value definition

Published on 30 Mar 2026 - 20:42

score 140 · Answer 10 · 2020-07-24 15:57:18

140

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Prove the series converges almost everywhere

Published on 24 Jul 2020 - 15:57

score 149 · Answer 11 · 2020-07-24 19:49:28

149

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Two sequences $f_n$ and $g_n$ such that $\int_{[0,1]}f_n g_n$ does not go to $0$ as $n\rightarrow\infty$, with these conditions on $f_n$ and $g_n$

Published on 24 Jul 2020 - 19:49

score 243 · Answer 12 · 2026-03-27 14:21:16

243

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Lebesgue Integration and Complex Integration

Published on 27 Mar 2026 - 14:21

score 72 · Answer 13 · 2020-07-25 20:46:34

72

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Prove that $m(\{x\in[0,1]:\lim \sup_{j\rightarrow\infty}f_j(x)\geq\frac{1}{2}\})\geq\frac{1}{2}$ under these conditions...

Published on 25 Jul 2020 - 20:46

score 307 · Answer 14 · 2020-07-25 22:40:10

Finding a dominating function to apply dominated convergence theorem on $\lim_{n\to \infty } \int_0^n (1-\frac{x}{n})^n \cos(\frac{x}{n})dx$

score 76 · Answer 15 · 2020-07-25 23:25:33

76

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A few questions regarding using Markov/Chebyshev and writing the Lebesgue measure in terms of the Lebesgue Integral

Published on 25 Jul 2020 - 23:25

List Question

$L^p$ Approximation of a $L^p$ function on $\Bbb R$ for $1\leq p<\infty$

Question regarding measure theory and Lebesgue integral

$f:[0,1]\rightarrow[0,1]$, measurable, and $\int_{[0,1]}f(x)dx=y\implies m\{x:f(x)>\frac{y}{2}\}\geq\frac{y}{2}$.

A question for a measurable function $g$ on a finite measure space such that $fg\in L^p$ for all $f\in L^p$

A question about measure theory.

Inequality concerning functions quadratic decay of distribution $m(|f|>\lambda)\leq C\lambda^{-2}$

Differentiating under the Integral with Carathéodory.

Rewrite $\int_{\mathbb{R^4}}\int_{\mathbb{R^4}}\ h(|x|^2,|y|^2,x\cdot y)\ dx\ dy$ as $\int\int\limits_{\Omega}\int\ J(u,v,w)\ h(u,v,w)\ du\ dv\ dw$.

Explain how to translate Lebesgue to Riemann integral in expected value definition

Prove the series converges almost everywhere

Two sequences $f_n$ and $g_n$ such that $\int_{[0,1]}f_n g_n$ does not go to $0$ as $n\rightarrow\infty$, with these conditions on $f_n$ and $g_n$

Lebesgue Integration and Complex Integration

Prove that $m(\{x\in[0,1]:\lim \sup_{j\rightarrow\infty}f_j(x)\geq\frac{1}{2}\})\geq\frac{1}{2}$ under these conditions...

Finding a dominating function to apply dominated convergence theorem on $\lim_{n\to \infty } \int_0^n (1-\frac{x}{n})^n \cos(\frac{x}{n})dx$

A few questions regarding using Markov/Chebyshev and writing the Lebesgue measure in terms of the Lebesgue Integral

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