List questions from ergodic-theory

Published on 27 Mar 2026 - 10:07

223

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any stationary sequence can be embedded in a two-sided stationary sequence

Published on 13 Apr 2021 - 6:44

136

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Theorem 1.6 of peter walters' ergodic theory

Published on 13 Apr 2021 - 13:29

128

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Proving the Borell-Cantelli Lemma by martingale convergence theorem

Published on 14 Apr 2021 - 10:20

153

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$L^p$ convergence of certain "average" function

Published on 17 Apr 2021 - 0:17

71

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$\lim \frac{1}{n} \sum_{i=0}^{n-1} X \circ T^{i}$ T-invariant?

Published on 27 Mar 2026 - 18:09

77

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If $X\subset\mathbb R,f:X\rightarrow X: \forall I,J \subset X \exists n\in\mathbb N:J\subset f^n(I)$, then $f$ is Topologically Transitive.

Published on 28 Mar 2026 - 19:41

125

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Supremum of the integral over the compact and convex set belongs the extreme set

Published on 22 Apr 2021 - 18:53

63

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Surjective endomorphism, A, on a compact abelian group is ergodic if $\gamma A^n=\gamma$ implies $\gamma = 1$ for every character $\gamma$

Published on 30 Mar 2026 - 0:23

53

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Null measure on cylinder sets

Published on 28 Apr 2021 - 11:41

36

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A non-binary measure of ergodicity

Published on 28 Apr 2021 - 14:44

67

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On the ergodicity of $x(t)=x_1(t)+cX_2(t)$ in the mean

Published on 28 Apr 2021 - 20:00

356

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Convergence of Stationary random variables

Published on 27 Mar 2026 - 14:10

129

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Continuous ergodic measure preserving transformation thus transitive

Published on 30 Apr 2021 - 16:42

80

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(Exponential) Mixing for Gauss map - going from cylinders to intervals

Published on 26 Mar 2026 - 14:29

List Question

Regular outer measure resricted to a measurable subset

any stationary sequence can be embedded in a two-sided stationary sequence

Theorem 1.6 of peter walters' ergodic theory

Proving the Borell-Cantelli Lemma by martingale convergence theorem

$L^p$ convergence of certain "average" function

$\lim \frac{1}{n} \sum_{i=0}^{n-1} X \circ T^{i}$ T-invariant?

If $X\subset\mathbb R,f:X\rightarrow X: \forall I,J \subset X \exists n\in\mathbb N:J\subset f^n(I)$, then $f$ is Topologically Transitive.

Supremum of the integral over the compact and convex set belongs the extreme set

Surjective endomorphism, A, on a compact abelian group is ergodic if $\gamma A^n=\gamma$ implies $\gamma = 1$ for every character $\gamma$

Null measure on cylinder sets

A non-binary measure of ergodicity

On the ergodicity of $x(t)=x_1(t)+cX_2(t)$ in the mean

Convergence of Stationary random variables

Continuous ergodic measure preserving transformation thus transitive

(Exponential) Mixing for Gauss map - going from cylinders to intervals

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