Question

Fréchet derivative of the total variation norm for measures on a manifold

score 182 · Answer 1 · 2026-03-25 22:30:48

182

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Fréchet derivative of the total variation norm for measures on a manifold

Published on 25 Mar 2026 - 22:30

score 126 · Answer 2 · 2022-04-16 04:08:33

126

Views

Significance of Luzin's theorem.

Published on 16 Apr 2022 - 4:08

score 186 · Answer 3 · 2022-04-17 11:30:01

186

Views

approximating a measure by smooth measures

Published on 17 Apr 2022 - 11:30

score 39 · Answer 4 · 2022-04-22 11:36:45

39

Views

If $\mu_i(A) \to \mu(A)$ for all $A$ with $\mu(\partial A) = 0$, then $\int_E g \mathrm d \mu_i \to \int_E g \mathrm d \mu$

Published on 22 Apr 2022 - 11:36

score 191 · Answer 5 · 2022-04-22 17:09:30

191

Views

Triangle inequality of Prokhorov metric

Published on 22 Apr 2022 - 17:09

score 219 · Answer 6 · 2022-04-22 22:52:39

219

Views

Prokhorov metric can be extended to all finite Borel measures?

Published on 22 Apr 2022 - 22:52

score 131 · Answer 7 · 2022-04-23 00:35:19

131

Views

If the underlying metric space is separable, then weak convergence is equivalent to convergence in Prokhorov metric

Published on 23 Apr 2022 - 0:35

score 114 · Answer 8 · 2022-04-23 09:19:40

114

Views

The underlying metric space is separable if and only if the space of finite Borel measures is separable in Prokhorov metric

Published on 23 Apr 2022 - 9:19

score 1.6k · Answer 9 · 2026-03-27 02:34:16

1.6k

Views

Riesz-Markov theorem: any positive linear functional is continuous?

Published on 27 Mar 2026 - 2:34

score 16 · Answer 10 · 2026-03-07 08:56:26

16

Views

Let $\mu(X) = \infty$. Is the collection of Borel sets on which $\mu$ is both outer and inner regular a $\sigma$-algebra?

Published on 07 Mar 2026 - 8:56

score 491 · Answer 11 · 2026-02-23 10:22:29

491

Views

Every finite Borel measure on a separable metric space is tight.

Published on 23 Feb 2026 - 10:22

score 35 · Answer 12 · 2022-04-27 22:05:11

35

Views

A sufficient condition for a collection of Borel probability measures to be uniformly tight

Published on 27 Apr 2022 - 22:05

score 68 · Answer 13 · 2022-04-28 08:10:52

68

Views

The space of Borel probability measures is closed in that of finite Borel measures w.r.t. Lévy–Prokhorov metric

Published on 28 Apr 2022 - 8:10

score 139 · Answer 14 · 2022-04-28 12:36:26

139

Views

Compute explicitly Lévy–Prokhorov metric for $2$ finite Dirac measures

Published on 28 Apr 2022 - 12:36

score 31 · Answer 15 · 2022-04-28 15:03:43

31

Views

If either $\mathcal M(X)$ or $\mathcal P(X)$ is complete, then so is $X$

Published on 28 Apr 2022 - 15:03

List Question

Fréchet derivative of the total variation norm for measures on a manifold

Significance of Luzin's theorem.

approximating a measure by smooth measures

If $\mu_i(A) \to \mu(A)$ for all $A$ with $\mu(\partial A) = 0$, then $\int_E g \mathrm d \mu_i \to \int_E g \mathrm d \mu$

Triangle inequality of Prokhorov metric

Prokhorov metric can be extended to all finite Borel measures?

If the underlying metric space is separable, then weak convergence is equivalent to convergence in Prokhorov metric

The underlying metric space is separable if and only if the space of finite Borel measures is separable in Prokhorov metric

Riesz-Markov theorem: any positive linear functional is continuous?

Let $\mu(X) = \infty$. Is the collection of Borel sets on which $\mu$ is both outer and inner regular a $\sigma$-algebra?

Every finite Borel measure on a separable metric space is tight.

A sufficient condition for a collection of Borel probability measures to be uniformly tight

The space of Borel probability measures is closed in that of finite Borel measures w.r.t. Lévy–Prokhorov metric

Compute explicitly Lévy–Prokhorov metric for $2$ finite Dirac measures

If either $\mathcal M(X)$ or $\mathcal P(X)$ is complete, then so is $X$

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