List questions from lebesgue-measure

Published on 30 May 2019 - 11:34

757

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A subset of a Borel Set is Borel

Published on 30 May 2019 - 14:51

142

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Volume of compact rectangle in $\mathbb{R}^d$

Published on 30 May 2019 - 21:15

295

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Measurable function, $f$, with $\int_{(0,1)} |f(x)| dm(x) < \infty$ and $\int_{(0,1)} (f(x))^{2} dm(x) = \infty$?

Published on 01 Jun 2019 - 10:13

146

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Integrable function, show that its limit is 0

Published on 30 Mar 2026 - 1:44

197

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If f is a measurable function with $\int_{[0,1]}(f(x))^{2} dm(x) < \infty$ then $\int_{[0,1]}|f(x)| dm(x) < \infty$.

Published on 30 Mar 2026 - 3:39

976

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Lebesgue measurability of subset of the preimage of a measurable set under increasing absolutely continuous function

Published on 23 Feb 2026 - 4:57

72

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Calculating $ \lim_{n \rightarrow \infty} \int_{[1, \infty)} \frac{n \sin(\frac{x}{n}) }{x^3}\,dx$

Published on 30 Mar 2026 - 3:38

280

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Proof that a graph has lebesgue measure zero using fubini's thm

Published on 30 Mar 2026 - 3:37

46

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3-D Lebesgue measure of Menger sponge

Published on 27 Mar 2026 - 15:36

283

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Lebesgue measurability criterion

Published on 05 Jun 2019 - 13:58

204

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What is an m-null set?

Published on 06 Jun 2019 - 2:22

281

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Measure of a cone

Published on 31 Mar 2026 - 17:53

1k

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Measure of the set of numbers in $[0,1]$ without $3$ in their decimal expansions

Published on 25 Mar 2026 - 18:49

83

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If $\int_0^1f^k(x)\;dx\le M$, then $m(\{x\in[0,1]:f(x)>1\})=0$.

Published on 25 Mar 2026 - 20:11

List Question

Rudin proof of theorem 2.14 RCA inequality explanation

A subset of a Borel Set is Borel

Volume of compact rectangle in $\mathbb{R}^d$

Measurable function, $f$, with $\int_{(0,1)} |f(x)| dm(x) < \infty$ and $\int_{(0,1)} (f(x))^{2} dm(x) = \infty$?

Integrable function, show that its limit is 0

If f is a measurable function with $\int_{[0,1]}(f(x))^{2} dm(x) < \infty$ then $\int_{[0,1]}|f(x)| dm(x) < \infty$.

Lebesgue measurability of subset of the preimage of a measurable set under increasing absolutely continuous function

Calculating $ \lim_{n \rightarrow \infty} \int_{[1, \infty)} \frac{n \sin(\frac{x}{n}) }{x^3}\,dx$

Proof that a graph has lebesgue measure zero using fubini's thm

3-D Lebesgue measure of Menger sponge

Lebesgue measurability criterion

What is an m-null set?

Measure of a cone

Measure of the set of numbers in $[0,1]$ without $3$ in their decimal expansions

If $\int_0^1f^k(x)\;dx\le M$, then $m(\{x\in[0,1]:f(x)>1\})=0$.

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