Question

$\mathbb{Z}^2$-action on product is ergodic

score 65 · Answer 1 · 2026-04-11 21:58:19

65

Views

$\mathbb{Z}^2$-action on product is ergodic

Published on 11 Apr 2026 - 21:58

score 344 · Answer 2 · 2026-04-16 09:29:05

344

Views

Set of points where sequence of measurable functions is bounded from below and unbounded from above

Published on 16 Apr 2026 - 9:29

score 206 · Answer 3 · 2026-04-16 04:01:23

206

Views

Rewrite $ \int_{\mathcal{S}}dP_X=1 $ as conditions on boxes in $\mathbb{R}^d$

Published on 16 Apr 2026 - 4:01

score 241 · Answer 4 · 2026-04-12 09:10:31

241

Views

Why is it legitimate to assume that the Chapman-Kolmogorov equations hold everywhere?

Published on 12 Apr 2026 - 9:10

score 158 · Answer 5 · 2026-04-11 14:21:52

158

Views

Probability of union using conditional probabilities

Published on 11 Apr 2026 - 14:21

score 188 · Answer 6 · 2026-04-16 16:13:09

(Prove or Disprove) If $X$ is a metric space, then the Borel $\sigma$-algebra ${\cal B}_X$ contains every countable subset of $X$.

score 224 · Answer 7 · 2026-04-09 22:47:20

224

Views

Question about Jordan Measure

Published on 09 Apr 2026 - 22:47

score 372 · Answer 8 · 2026-04-10 20:59:53

372

Views

Definition of ergodic map

Published on 10 Apr 2026 - 20:59

score 56 · Answer 9 · 2026-04-12 13:30:18

56

Views

Is there a non-zero measure on $\mathbb{R}^2$ such that all subsets of $\mathbb{R}^2$ are measurable?

Published on 12 Apr 2026 - 13:30

score 3.3k · Answer 10 · 2026-05-10 19:38:37

3.3k

Views

What is the motivation of defining weak derivative as it is?

Published on 10 May 2026 - 19:38

score 187 · Answer 11 · 2026-04-14 08:46:48

187

Views

If $(κ_t)_{t≥0}$ is the transition semigroup of a continuous Markov process, is $t↦(κ_tf)(x)$ continuous for all bounded continuous $f$ and fixed $x$?

Published on 14 Apr 2026 - 8:46

score 33 · Answer 12 · 2026-04-10 05:21:37

33

Views

A question about the outer measure generated

Published on 10 Apr 2026 - 5:21

score 116 · Answer 13 · 2026-04-14 05:52:29

116

Views

Show that two Markov kernels almost surely agree

Published on 14 Apr 2026 - 5:52

score 47 · Answer 14 · 2026-05-10 19:16:50

47

Views

Does this conclude that $ \int_E f_jg_j dx \to \int_E fgdx$?

Published on 10 May 2026 - 19:16

score 74 · Answer 15 · 2026-04-15 17:40:52

74

Views

How can I show $\int_{U}\frac{\partial f}{\partial x_{i}}(x)g(x)d\lambda^{d}(x)=-\int_{U}f(x)\frac{\partial g}{\partial x_{i}}(x)d\lambda^{d}(x)$

Published on 15 Apr 2026 - 17:40

List Question

$\mathbb{Z}^2$-action on product is ergodic

Set of points where sequence of measurable functions is bounded from below and unbounded from above

Rewrite $ \int_{\mathcal{S}}dP_X=1 $ as conditions on boxes in $\mathbb{R}^d$

Why is it legitimate to assume that the Chapman-Kolmogorov equations hold everywhere?

Probability of union using conditional probabilities

(Prove or Disprove) If $X$ is a metric space, then the Borel $\sigma$-algebra ${\cal B}_X$ contains every countable subset of $X$.

Question about Jordan Measure

Definition of ergodic map

Is there a non-zero measure on $\mathbb{R}^2$ such that all subsets of $\mathbb{R}^2$ are measurable?

What is the motivation of defining weak derivative as it is?

If $(κ_t)_{t≥0}$ is the transition semigroup of a continuous Markov process, is $t↦(κ_tf)(x)$ continuous for all bounded continuous $f$ and fixed $x$?

A question about the outer measure generated

Show that two Markov kernels almost surely agree

Does this conclude that $ \int_E f_jg_j dx \to \int_E fgdx$?

How can I show $\int_{U}\frac{\partial f}{\partial x_{i}}(x)g(x)d\lambda^{d}(x)=-\int_{U}f(x)\frac{\partial g}{\partial x_{i}}(x)d\lambda^{d}(x)$

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