Question

If $c_n \nearrow c$ then $\lim_n \inf_{\pi \in \Pi(\mu, \nu)} \int c_n d\pi = \inf_{\pi \in \Pi(\mu, \nu)} \int c d\pi$

score 45 · Answer 1 · 2022-05-17 14:30:24

45

Views

If $c_n \nearrow c$ then $\lim_n \inf_{\pi \in \Pi(\mu, \nu)} \int c_n d\pi = \inf_{\pi \in \Pi(\mu, \nu)} \int c d\pi$

Published on 17 May 2022 - 14:30

score 24 · Answer 2 · 2026-02-23 10:02:32

24

Views

Homeomorphism between $\mathbb N^\infty$ and a closed subset $\mathbb M$ of $(\mathbb N^\infty)^\infty$

Published on 23 Feb 2026 - 10:02

score 64 · Answer 3 · 2022-07-06 15:39:16

64

Views

Is the $c$-transform $f^c$ defined by $f^c(y) := \inf_{x\in X} [c(x, y)- f(x)]$ measurable?

Published on 06 Jul 2022 - 15:39

score 98 · Answer 4 · 2022-07-25 18:52:02

98

Views

On morphisms and equivalence of Polish Spaces

Published on 25 Jul 2022 - 18:52

score 71 · Answer 5 · 2022-08-27 03:51:01

71

Views

Let $\mu$ be a Borel measure and $x_n \to x$. Is it true that $\mu (B(x_n, r)) \to \mu (B(x, r))$?

Published on 27 Aug 2022 - 3:51

score 67 · Answer 6 · 2022-08-30 18:31:38

67

Views

Examples of dense and codense $G_\delta$ subsets of $\mathbb{R}^2$ that are not homeomorphic to $\mathcal{N}=\mathbb{N}^\mathbb{N}$

Published on 30 Aug 2022 - 18:31

score 70 · Answer 7 · 2022-09-07 00:13:54

70

Views

Is Homeo$(X)$ a $G_\delta$ subset of $C(X,X)$?

Published on 07 Sep 2022 - 0:13

score 50 · Answer 8 · 2022-10-11 15:20:17

50

Views

Where completeness and separability are used in a proof of this lemma?

Published on 11 Oct 2022 - 15:20

score 234 · Answer 9 · 2022-10-28 15:53:06

234

Views

Disintegration theorem: how do the authors prove that $\mu_y$ is supported on $\pi^{-1} (y)$ for $\nu$-a.e. $y \in Y$?

Published on 28 Oct 2022 - 15:53

score 74 · Answer 10 · 2022-10-30 13:46:11

74

Views

How to prove these definitions of an analytic set are equivalent?

Published on 30 Oct 2022 - 13:46

score 83 · Answer 11 · 2022-11-19 00:34:00

83

Views

How does the use of disintegration theorem make sense here?

Published on 19 Nov 2022 - 0:34

score 50 · Answer 12 · 2022-11-19 09:34:36

50

Views

How to construct a measurable map $\psi'$ such that $\psi' = \psi$ $\nu$-a.e.?

Published on 19 Nov 2022 - 9:34

score 39 · Answer 13 · 2022-11-19 22:43:48

39

Views

The existence of a $\sigma$-compact set with full probability

Published on 19 Nov 2022 - 22:43

score 105 · Answer 14 · 2022-11-30 12:21:43

105

Views

Compact vs. Polish space in application field.

Published on 30 Nov 2022 - 12:21

score 116 · Answer 15 · 2022-12-23 17:19:03

116

Views

Definition of Polish space: why homeomorphic?

Published on 23 Dec 2022 - 17:19

List Question

If $c_n \nearrow c$ then $\lim_n \inf_{\pi \in \Pi(\mu, \nu)} \int c_n d\pi = \inf_{\pi \in \Pi(\mu, \nu)} \int c d\pi$

Homeomorphism between $\mathbb N^\infty$ and a closed subset $\mathbb M$ of $(\mathbb N^\infty)^\infty$

Is the $c$-transform $f^c$ defined by $f^c(y) := \inf_{x\in X} [c(x, y)- f(x)]$ measurable?

On morphisms and equivalence of Polish Spaces

Let $\mu$ be a Borel measure and $x_n \to x$. Is it true that $\mu (B(x_n, r)) \to \mu (B(x, r))$?

Examples of dense and codense $G_\delta$ subsets of $\mathbb{R}^2$ that are not homeomorphic to $\mathcal{N}=\mathbb{N}^\mathbb{N}$

Is Homeo$(X)$ a $G_\delta$ subset of $C(X,X)$?

Where completeness and separability are used in a proof of this lemma?

Disintegration theorem: how do the authors prove that $\mu_y$ is supported on $\pi^{-1} (y)$ for $\nu$-a.e. $y \in Y$?

How to prove these definitions of an analytic set are equivalent?

How does the use of disintegration theorem make sense here?

How to construct a measurable map $\psi'$ such that $\psi' = \psi$ $\nu$-a.e.?

The existence of a $\sigma$-compact set with full probability

Compact vs. Polish space in application field.

Definition of Polish space: why homeomorphic?

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