List questions from ergodic-theory

Published on 12 Apr 2026 - 1:27

72

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Spectral Invariants

Published on 30 Apr 2026 - 9:58

144

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A strengthened implication of the ergodicity

Published on 14 Apr 2026 - 7:38

63

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If $T:[0,1] \rightarrow [0,1]$ preserves Lebesgue, then $\liminf_n(n|T^n(x)-x|) \leq 1$

Published on 14 Apr 2026 - 21:02

425

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On the definition of ergodicity and how it relates to random processes.

Published on 14 Apr 2026 - 6:02

97

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About definition of Ergodic theorem

Published on 09 Apr 2026 - 9:54

505

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Example of measures being ergodic but not invariant

Published on 12 Apr 2026 - 2:49

230

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Counterexample for the $L^p$ Ergodic Theorem of Von Neumann when $p=\infty$

Published on 12 Apr 2026 - 20:33

120

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Entropy Theory and Conditional Entropy

Published on 13 Apr 2026 - 6:15

182

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Trouble understanding the proof of disintegration of measure by Tao

Published on 12 Apr 2026 - 3:58

290

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Measurability with respect to the $\sigma$-algebra of invariant sets.

Published on 16 Apr 2026 - 6:42

123

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"Two step" Markov chain is actually a Markov chian

Published on 10 Apr 2026 - 16:45

113

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Compact, infinite, invariant set on shift space.

Published on 12 Apr 2026 - 5:02

109

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Proving Conservativeness directly from Maharam's theorem

Published on 14 Apr 2026 - 18:20

59

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In a Banach space $x_n\text{cos}(nt)+ y_n\text{sin}{nt}\rightarrow 0$ implies both sequences individually go to $0$.

Published on 15 Apr 2026 - 22:03

List Question

The Generalisations of Ergodic Theorems

Spectral Invariants

A strengthened implication of the ergodicity

If $T:[0,1] \rightarrow [0,1]$ preserves Lebesgue, then $\liminf_n(n|T^n(x)-x|) \leq 1$

On the definition of ergodicity and how it relates to random processes.

About definition of Ergodic theorem

Example of measures being ergodic but not invariant

Counterexample for the $L^p$ Ergodic Theorem of Von Neumann when $p=\infty$

Entropy Theory and Conditional Entropy

Trouble understanding the proof of disintegration of measure by Tao

Measurability with respect to the $\sigma$-algebra of invariant sets.

"Two step" Markov chain is actually a Markov chian

Compact, infinite, invariant set on shift space.

Proving Conservativeness directly from Maharam's theorem

In a Banach space $x_n\text{cos}(nt)+ y_n\text{sin}{nt}\rightarrow 0$ implies both sequences individually go to $0$.

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