Question

Formula relating the volume of a unit $n$-ball and surface area of a unit $n-1$-sphere when $n = 1$

score 61 · Answer 1 · 2026-03-27 14:03:20

61

Views

Formula relating the volume of a unit $n$-ball and surface area of a unit $n-1$-sphere when $n = 1$

Published on 27 Mar 2026 - 14:03

score 820 · Answer 2 · 2026-04-03 04:22:07

820

Views

Prove graph of measurable function is measurable in $\sigma$-finite case and that the product measure is $0$.

Published on 03 Apr 2026 - 4:22

score 97 · Answer 3 · 2026-04-11 06:29:19

97

Views

Find an example given Hypotheses , DCT does not hold

Published on 11 Apr 2026 - 6:29

score 32 · Answer 4 · 2026-04-03 04:21:03

32

Views

For which $p\geq 1$ is $0=\lim_{n\rightarrow \infty} \bigg( \int |n\cdot 1_{[n,n+1/n^2]}|^p \bigg)^{1/p}$

Published on 03 Apr 2026 - 4:21

score 108 · Answer 5 · 2026-04-03 05:47:09

108

Views

MCT, DCT, and Fatou's Lemma related problems Bank

Published on 03 Apr 2026 - 5:47

score 175 · Answer 6 · 2019-10-27 00:00:27

175

Views

If $\lim_{n\to \infty}\mu(B_n\setminus A_n )= 0 \& A_n\subset E\subset B_n$, then is $E$ measurable?

Published on 27 Oct 2019 - 0:00

score 398 · Answer 7 · 2026-04-11 09:16:07

398

Views

Does any interval between points in Fat Cantor set have positive measure

Published on 11 Apr 2026 - 9:16

score 87 · Answer 8 · 2019-10-27 18:36:54

87

Views

$\{x \in \mathbb{R} : f$ is Lebesgue integrable in some open neighborhood of $x\}$ is dense in $\mathbb{R}$.

Published on 27 Oct 2019 - 18:36

score 97 · Answer 9 · 2019-10-27 22:09:52

97

Views

if $\lambda(A)>1$, then $\exists x, y \in A , (x - y) \in \mathbb{N}$

Published on 27 Oct 2019 - 22:09

score 655 · Answer 10 · 2019-10-27 23:51:12

655

Views

Lebesgue measure is the completion of a product of Lebesgue measures

Published on 27 Oct 2019 - 23:51

score 180 · Answer 11 · 2026-03-30 15:32:08

180

Views

Universal properties in measure theory and probabilities

Published on 30 Mar 2026 - 15:32

score 100 · Answer 12 · 2019-10-29 01:17:24

100

Views

Criterion for Lebesgue measurability involving $m^*(O-F) < \epsilon$

Published on 29 Oct 2019 - 1:17

score 74 · Answer 13 · 2019-10-29 03:06:45

74

Views

Is it true that if E is measurable set and f is continuous on E, $B \subseteq \Bbb R$ a measurable set, then $f^{-1}(B)$ measurable?

Published on 29 Oct 2019 - 3:06

score 259 · Answer 14 · 2026-03-29 04:47:23

259

Views

$f \in \mathscr{R}[a,b] \implies |f| \in \mathscr{R}[a,b]$

Published on 29 Mar 2026 - 4:47

score 179 · Answer 15 · 2026-04-08 23:31:04

179

Views

Is $I$ Lebesgue integrable?

Published on 08 Apr 2026 - 23:31

List Question

Formula relating the volume of a unit $n$-ball and surface area of a unit $n-1$-sphere when $n = 1$

Prove graph of measurable function is measurable in $\sigma$-finite case and that the product measure is $0$.

Find an example given Hypotheses , DCT does not hold

For which $p\geq 1$ is $0=\lim_{n\rightarrow \infty} \bigg( \int |n\cdot 1_{[n,n+1/n^2]}|^p \bigg)^{1/p}$

MCT, DCT, and Fatou's Lemma related problems Bank

If $\lim_{n\to \infty}\mu(B_n\setminus A_n )= 0 \& A_n\subset E\subset B_n$, then is $E$ measurable?

Does any interval between points in Fat Cantor set have positive measure

$\{x \in \mathbb{R} : f$ is Lebesgue integrable in some open neighborhood of $x\}$ is dense in $\mathbb{R}$.

if $\lambda(A)>1$, then $\exists x, y \in A , (x - y) \in \mathbb{N}$

Lebesgue measure is the completion of a product of Lebesgue measures

Universal properties in measure theory and probabilities

Criterion for Lebesgue measurability involving $m^*(O-F) < \epsilon$

Is it true that if E is measurable set and f is continuous on E, $B \subseteq \Bbb R$ a measurable set, then $f^{-1}(B)$ measurable?

$f \in \mathscr{R}[a,b] \implies |f| \in \mathscr{R}[a,b]$

Is $I$ Lebesgue integrable?

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