Question

How to prove that $\text{area}( S_r(x) \cap B_R(0)) \leq \text{area}(S_R(0))$?

score 112 · Answer 1 · 2026-05-11 08:39:26

112

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How to prove that $\text{area}( S_r(x) \cap B_R(0)) \leq \text{area}(S_R(0))$?

Published on 11 May 2026 - 8:39

score 86 · Answer 2 · 2026-04-16 21:32:05

86

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Why $\mathbb P(X_t=Y_t\text{ for all }t)=1$ if $\mathbb P(X_t=Y_t)=1$ for all $t$?

Published on 16 Apr 2026 - 21:32

score 65 · Answer 3 · 2026-04-14 07:03:51

65

Views

Why it mustn't be a sigma algebra?

Published on 14 Apr 2026 - 7:03

score 87 · Answer 4 · 2026-05-10 16:58:46

87

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Function with the property $f\circ f=-id$

Published on 10 May 2026 - 16:58

score 999 · Answer 5 · 2026-04-11 05:13:20

999

Views

infinite sum as integral for the counting measure

Published on 11 Apr 2026 - 5:13

score 148 · Answer 6 · 2026-04-16 11:42:55

Example of almost surely continuous stochastic process $(X_t)$ with $\{\omega \mid t\mapsto X_t(\omega )\text{ continuous}\}$ non measurable?

score 29 · Answer 7 · 2026-05-11 04:06:51

29

Views

$\int x^k\ d\mu(x)\geq0$ for $k$ even?

Published on 11 May 2026 - 4:06

score 163 · Answer 8 · 2026-04-14 00:34:53

163

Views

Prove there exists a measurable subset $E' \subset E$ such that $f$ is almost everywhere of one sign on $E'$.

Published on 14 Apr 2026 - 0:34

score 38 · Answer 9 · 2026-04-11 19:09:51

38

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If $\mathcal N$ non measurable, $\{0\}\times \mathcal N$ is measurable in $\mathbb R^2$, but $m(\{0\}\times \mathcal N)$

Published on 11 Apr 2026 - 19:09

score 227 · Answer 10 · 2026-04-12 08:08:11

227

Views

Hint on measure theory problem about rational-invariant measurable sets

Published on 12 Apr 2026 - 8:08

score 1.3k · Answer 11 · 2026-04-12 11:32:49

1.3k

Views

Dilatation of a measurable set is a measurable set.

Published on 12 Apr 2026 - 11:32

score 119 · Answer 12 · 2026-04-14 06:20:01

119

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Picking up a random element of $\mathcal P(\mathbb R)$: existence of probability measure?

Published on 14 Apr 2026 - 6:20

score 1.2k · Answer 13 · 2026-04-16 13:48:54

1.2k

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Showing $B$ Borel set, then $f^{-1}(B)$ is a Borel set with $f$ continuous function.

Published on 16 Apr 2026 - 13:48

score 311 · Answer 14 · 2026-04-15 09:43:52

311

Views

Understanding Folland 3.9 Proposition: Radon-Nikodym Derivative

Published on 15 Apr 2026 - 9:43

score 42 · Answer 15 · 2026-04-13 07:20:42

42

Views

Question on redefinition of an expectation

Published on 13 Apr 2026 - 7:20

List Question

How to prove that $\text{area}( S_r(x) \cap B_R(0)) \leq \text{area}(S_R(0))$?

Why $\mathbb P(X_t=Y_t\text{ for all }t)=1$ if $\mathbb P(X_t=Y_t)=1$ for all $t$?

Why it mustn't be a sigma algebra?

Function with the property $f\circ f=-id$

infinite sum as integral for the counting measure

Example of almost surely continuous stochastic process $(X_t)$ with $\{\omega \mid t\mapsto X_t(\omega )\text{ continuous}\}$ non measurable?

$\int x^k\ d\mu(x)\geq0$ for $k$ even?

Prove there exists a measurable subset $E' \subset E$ such that $f$ is almost everywhere of one sign on $E'$.

If $\mathcal N$ non measurable, $\{0\}\times \mathcal N$ is measurable in $\mathbb R^2$, but $m(\{0\}\times \mathcal N)$

Hint on measure theory problem about rational-invariant measurable sets

Dilatation of a measurable set is a measurable set.

Picking up a random element of $\mathcal P(\mathbb R)$: existence of probability measure?

Showing $B$ Borel set, then $f^{-1}(B)$ is a Borel set with $f$ continuous function.

Understanding Folland 3.9 Proposition: Radon-Nikodym Derivative

Question on redefinition of an expectation

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