Question

Interesting relationship between cardinality and Lebesgue outer measure

score 191 · Answer 1 · 2026-04-09 00:51:21

191

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Interesting relationship between cardinality and Lebesgue outer measure

Published on 09 Apr 2026 - 0:51

score 227 · Answer 2 · 2026-04-13 13:45:13

227

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Why is the fact true that if $E$ has measure zero, then $E_a$ has measure zero?

Published on 13 Apr 2026 - 13:45

score 114 · Answer 3 · 2026-04-11 14:55:41

114

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Calculate limit with integral

Published on 11 Apr 2026 - 14:55

score 1.6k · Answer 4 · 2026-04-15 06:13:26

1.6k

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If $f$ is nonnegative and integrable then $F(x) = \int_{-\infty}^x f$ is continuous.

Published on 15 Apr 2026 - 6:13

score 516 · Answer 5 · 2026-03-25 23:35:49

516

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Understanding principal value integral

Published on 25 Mar 2026 - 23:35

score 3.7k · Answer 6 · 2026-04-15 17:11:07

3.7k

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translation invariant of integral on $\mathbb{R}$

Published on 15 Apr 2026 - 17:11

score 343 · Answer 7 · 2026-04-18 08:42:05

343

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Is the charateristic function $\chi _{\Omega }$ in the Sobolev space $W^{1,2}_{0}(\Omega)$?

Published on 18 Apr 2026 - 8:42

score 77 · Answer 8 · 2026-04-16 09:23:46

77

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Regularity of a measure $n(E) = \int_{E} f(x) dx$

Published on 16 Apr 2026 - 9:23

score 47 · Answer 9 · 2026-04-15 19:09:04

47

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Is this intuitive true that $\int_Ef=\int_{I_n}f$

Published on 15 Apr 2026 - 19:09

score 575 · Answer 10 · 2026-04-16 01:51:52

575

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Does $f_n \rightarrow f$ $\mu$-a.e. and $\lim \int f_n \rightarrow \int f$ imply $f_n \rightarrow f$ in $L^1(\mu)$?

Published on 16 Apr 2026 - 1:51

score 122 · Answer 11 · 2026-04-10 00:42:16

122

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Lebesgue Integral over vanishing interval

Published on 10 Apr 2026 - 0:42

score 334 · Answer 12 · 2026-04-12 22:50:53

334

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Convergence of sequence of smooth functions

Published on 12 Apr 2026 - 22:50

score 98 · Answer 13 · 2026-04-17 15:04:11

98

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Where $f:[0,1]\to\mathbb R$ is Lebesgue integrable, show $\lim_{n\to\infty} n\lambda(\{x:|f(x)|\geq n\})=0$.

Published on 17 Apr 2026 - 15:04

score 1.9k · Answer 14 · 2026-04-16 10:04:39

1.9k

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$\int_\Omega f d\mu = 0 $ if and only if $f(x)=0$ almost everywhere

Published on 16 Apr 2026 - 10:04

score 164 · Answer 15 · 2026-04-05 22:38:54

164

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Lebesgue Integral-Question

Published on 05 Apr 2026 - 22:38

List Question

Interesting relationship between cardinality and Lebesgue outer measure

Why is the fact true that if $E$ has measure zero, then $E_a$ has measure zero?

Calculate limit with integral

If $f$ is nonnegative and integrable then $F(x) = \int_{-\infty}^x f$ is continuous.

Understanding principal value integral

translation invariant of integral on $\mathbb{R}$

Is the charateristic function $\chi _{\Omega }$ in the Sobolev space $W^{1,2}_{0}(\Omega)$?

Regularity of a measure $n(E) = \int_{E} f(x) dx$

Is this intuitive true that $\int_Ef=\int_{I_n}f$

Does $f_n \rightarrow f$ $\mu$-a.e. and $\lim \int f_n \rightarrow \int f$ imply $f_n \rightarrow f$ in $L^1(\mu)$?

Lebesgue Integral over vanishing interval

Convergence of sequence of smooth functions

Where $f:[0,1]\to\mathbb R$ is Lebesgue integrable, show $\lim_{n\to\infty} n\lambda(\{x:|f(x)|\geq n\})=0$.

$\int_\Omega f d\mu = 0 $ if and only if $f(x)=0$ almost everywhere

Lebesgue Integral-Question

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