List questions from lebesgue-measure

Published on 12 Apr 2026 - 15:47

63

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Verify $\lim_{n\rightarrow \infty}f_n(x)=x^{-1/2}$ almost always in $[0,1]$ and $\lim_{n\rightarrow\infty}\int^1_0f_n(x)=\int^1_0 \frac{dx}{x^2}$

Published on 17 Apr 2026 - 0:54

78

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Is $g$ bounded variation in [-1,1]?

Published on 10 Apr 2026 - 22:54

225

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Existence of continuous function on compact interval

Published on 07 Apr 2026 - 22:15

76

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showing that $\lim_{n\to\infty}\int_{-n}^{n}f=\lim_{n\to\infty}\int _{\{f\leq n\}}f$

Published on 15 Apr 2026 - 16:07

206

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Is the domain of the symmetric derivative of a borel measure a borel set?

Published on 14 Apr 2026 - 13:45

84

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Limit of a sequence of measurable function.

Published on 11 Apr 2026 - 18:15

215

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Lebesgue-Stieltjes measurable set.

Published on 13 Apr 2026 - 15:01

71

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Series convergence in $L_p$

Published on 14 Apr 2026 - 6:59

142

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Example of $L^p$ function which does not have much Lebesgue points

Published on 11 Apr 2026 - 19:16

134

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All the functions $\phi$ such that $\phi (\lim_{p\to 0}||f||_p)=\int_0^1 (\phi of)dm$

Published on 17 Apr 2026 - 13:00

473

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How to show that $\mu$ is $\sigma$-finite

Published on 11 Apr 2026 - 1:05

504

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A descending sequence of sets with outer measure 1

Published on 14 Apr 2026 - 1:07

89

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Inequality of the $L_p$ spaces

Published on 16 Apr 2026 - 19:36

228

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0 integral means vanishing f ae

Published on 16 Apr 2026 - 8:20

List Question

How to prove that a function is in fact $L_1$?

Verify $\lim_{n\rightarrow \infty}f_n(x)=x^{-1/2}$ almost always in $[0,1]$ and $\lim_{n\rightarrow\infty}\int^1_0f_n(x)=\int^1_0 \frac{dx}{x^2}$

Is $g$ bounded variation in [-1,1]?

Existence of continuous function on compact interval

showing that $\lim_{n\to\infty}\int_{-n}^{n}f=\lim_{n\to\infty}\int _{\{f\leq n\}}f$

Is the domain of the symmetric derivative of a borel measure a borel set?

Limit of a sequence of measurable function.

Lebesgue-Stieltjes measurable set.

Series convergence in $L_p$

Example of $L^p$ function which does not have much Lebesgue points

All the functions $\phi$ such that $\phi (\lim_{p\to 0}||f||_p)=\int_0^1 (\phi of)dm$

How to show that $\mu$ is $\sigma$-finite

A descending sequence of sets with outer measure 1

Inequality of the $L_p$ spaces

0 integral means vanishing f ae

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