Question

If average of an $L^1$ function is in S, then does $f \in S$?

score 59 · Answer 1 · 2026-04-13 17:07:42

59

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If average of an $L^1$ function is in S, then does $f \in S$?

Published on 13 Apr 2026 - 17:07

score 736 · Answer 2 · 2026-04-13 00:35:32

736

Views

Proving cumulative distribution function is right-continuous and have limits 0 and 1

Published on 13 Apr 2026 - 0:35

score 120 · Answer 3 · 2026-04-15 19:28:10

120

Views

Show that $\int_E f d\mu=0$ if $\mu(E)=0$.

Published on 15 Apr 2026 - 19:28

score 180 · Answer 4 · 2026-04-16 15:58:47

180

Views

Prove $\lim_{r \to 0} \frac{1}{2r} \int_{x-r}^{x+r} f(z) dz = f(x)$

Published on 16 Apr 2026 - 15:58

score 103 · Answer 5 · 2026-04-16 12:09:57

103

Views

In Wasserstein, what is the relationship between $W_2 (\widehat{\mathbb{P}}_{N},\mathbb{P})$ and $W_2 (\widehat{\mathbb{P}}_{N}^{x},\mathbb{P}^{x})$?

Published on 16 Apr 2026 - 12:09

score 954 · Answer 6 · 2026-04-13 13:37:35

954

Views

Lebesgue integral of the extended Cantor function

Published on 13 Apr 2026 - 13:37

score 375 · Answer 7 · 2026-04-11 05:20:41

375

Views

Is Girsanov the only way to change measure?

Published on 11 Apr 2026 - 5:20

score 657 · Answer 8 · 2026-04-14 21:58:22

657

Views

Lebesgue integral of a function that is measurable, finite almost everywhere, and integrable on a set of finite measure

Published on 14 Apr 2026 - 21:58

score 708 · Answer 9 · 2026-04-17 02:30:27

708

Views

Levy's construction of Brownian Motion

Published on 17 Apr 2026 - 2:30

score 38 · Answer 10 · 2026-04-14 05:53:12

38

Views

Why $\mu_1$ satisfy the following property?

Published on 14 Apr 2026 - 5:53

score 36 · Answer 11 · 2026-04-15 05:05:58

36

Views

Outer measure of the set $A= \lbrace x \in \mathbb{R}^n :\exists r>0 \; with \; \mu(B_r(x))=0 \rbrace$

Published on 15 Apr 2026 - 5:05

score 57 · Answer 12 · 2026-04-12 02:49:33

57

Views

Integral over product space with one singularity is finite

Published on 12 Apr 2026 - 2:49

score 103 · Answer 13 · 2026-04-06 01:05:40

103

Views

What is the meaning of vector measures?

Published on 06 Apr 2026 - 1:05

score 48 · Answer 14 · 2026-04-15 04:22:47

48

Views

Sigma-field under a certain probability measure

Published on 15 Apr 2026 - 4:22

score 315 · Answer 15 · 2026-04-14 14:26:14

315

Views

An counterexample for the monotone convergence theorem and dominated convergence theorem

Published on 14 Apr 2026 - 14:26

List Question

If average of an $L^1$ function is in S, then does $f \in S$?

Proving cumulative distribution function is right-continuous and have limits 0 and 1

Show that $\int_E f d\mu=0$ if $\mu(E)=0$.

Prove $\lim_{r \to 0} \frac{1}{2r} \int_{x-r}^{x+r} f(z) dz = f(x)$

In Wasserstein, what is the relationship between $W_2 (\widehat{\mathbb{P}}_{N},\mathbb{P})$ and $W_2 (\widehat{\mathbb{P}}_{N}^{x},\mathbb{P}^{x})$?

Lebesgue integral of the extended Cantor function

Is Girsanov the only way to change measure?

Lebesgue integral of a function that is measurable, finite almost everywhere, and integrable on a set of finite measure

Levy's construction of Brownian Motion

Why $\mu_1$ satisfy the following property?

Outer measure of the set $A= \lbrace x \in \mathbb{R}^n :\exists r>0 \; with \; \mu(B_r(x))=0 \rbrace$

Integral over product space with one singularity is finite

What is the meaning of vector measures?

Sigma-field under a certain probability measure

An counterexample for the monotone convergence theorem and dominated convergence theorem

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