Question

Product measure and decomposition of measure

score 78 · Answer 1 · 2026-04-11 12:32:31

78

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Product measure and decomposition of measure

Published on 11 Apr 2026 - 12:32

score 842 · Answer 2 · 2026-04-13 05:21:27

842

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Question on the proof that the Cantor set has measure zero

Published on 13 Apr 2026 - 5:21

score 54 · Answer 3 · 2026-04-13 08:55:03

54

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About alternative definition of $s$-dimensional Hausdorff outer measure in $\Bbb R^n$

Published on 13 Apr 2026 - 8:55

score 218 · Answer 4 · 2026-04-11 11:10:01

218

Views

Finding the closed support of a probability measure

Published on 11 Apr 2026 - 11:10

score 218 · Answer 5 · 2026-04-09 08:06:53

218

Views

Pointwise convergence in limit of conditional probabilities implies almost sure convergence?

Published on 09 Apr 2026 - 8:06

score 339 · Answer 6 · 2026-04-16 20:23:00

339

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If $B \subset A \subset \mathbb{R}$ such that $m^(B)=0 $. Show that $m^(A \setminus B)=m^*(A)$.

Published on 16 Apr 2026 - 20:23

score 231 · Answer 7 · 2026-04-16 05:04:47

231

Views

Distance between probability measures supported in different dimensions

Published on 16 Apr 2026 - 5:04

score 173 · Answer 8 · 2026-04-16 01:06:18

If $A \subset B \subset \mathbb{R}$ such that $A$ is Lebesgue measurable and $m^*(B)=m(A)< \infty$. Show that $B$ is Lebesgue measurable.

score 200 · Answer 9 · 2026-04-12 02:21:48

200

Views

$\sum \xi_n<\infty \;\text{a.e.}\; \rightarrow \sum \sigma_n^2 < \infty$ if $E(\xi_n)=0$ and $V(\xi_n)=\sigma_n^2<\infty$.

Published on 12 Apr 2026 - 2:21

score 561 · Answer 10 · 2026-03-25 03:07:07

561

Views

Why is Hausdorff dimension monotonic?

Published on 25 Mar 2026 - 3:07

score 50 · Answer 11 · 2026-04-16 03:23:55

50

Views

If $A,B \subset \mathbb{R} $ such that $m^*(A)=0 $ and $A \cup B$ is Lebesgue measurable. Show that $B$ is Lebesgue measurable.

Published on 16 Apr 2026 - 3:23

score 78 · Answer 12 · 2026-04-18 22:01:48

78

Views

Approximating measurable functions by simple functions on measurable sets.

Published on 18 Apr 2026 - 22:01

score 349 · Answer 13 · 2026-04-09 05:30:02

349

Views

The Dual of $L^{\infty}$ and the Radon-Nikodym Theorem

Published on 09 Apr 2026 - 5:30

score 479 · Answer 14 · 2026-04-18 23:29:45

479

Views

Prove a collection of sets measure 0 or 1 is a $\sigma$-algebra

Published on 18 Apr 2026 - 23:29

score 177 · Answer 15 · 2026-04-11 04:36:12

177

Views

Brownian sheet as a martingale measure.

Published on 11 Apr 2026 - 4:36

List Question

Product measure and decomposition of measure

Question on the proof that the Cantor set has measure zero

About alternative definition of $s$-dimensional Hausdorff outer measure in $\Bbb R^n$

Finding the closed support of a probability measure

Pointwise convergence in limit of conditional probabilities implies almost sure convergence?

If $B \subset A \subset \mathbb{R}$ such that $m^(B)=0 $. Show that $m^(A \setminus B)=m^*(A)$.

Distance between probability measures supported in different dimensions

If $A \subset B \subset \mathbb{R}$ such that $A$ is Lebesgue measurable and $m^*(B)=m(A)< \infty$. Show that $B$ is Lebesgue measurable.

$\sum \xi_n<\infty \;\text{a.e.}\; \rightarrow \sum \sigma_n^2 < \infty$ if $E(\xi_n)=0$ and $V(\xi_n)=\sigma_n^2<\infty$.

Why is Hausdorff dimension monotonic?

If $A,B \subset \mathbb{R} $ such that $m^*(A)=0 $ and $A \cup B$ is Lebesgue measurable. Show that $B$ is Lebesgue measurable.

Approximating measurable functions by simple functions on measurable sets.

The Dual of $L^{\infty}$ and the Radon-Nikodym Theorem

Prove a collection of sets measure 0 or 1 is a $\sigma$-algebra

Brownian sheet as a martingale measure.

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