Question

Prove that $T$ is ergodic if $\mu(T^{-n}A \cap B)>0$

score 122 · Answer 1 · 2018-02-26 20:47:36

122

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Prove that $T$ is ergodic if $\mu(T^{-n}A \cap B)>0$

Published on 26 Feb 2018 - 20:47

score 42 · Answer 2 · 2026-03-25 01:27:25

42

Views

Does, under iteration, all strongly mixing transformations tend to spread sets out, not only in (ordinary) diameter, but also in harmonic diameter?

Published on 25 Mar 2026 - 1:27

score 199 · Answer 3 · 2026-03-22 07:36:12

199

Views

Density limits and sets with positive lower density

Published on 22 Mar 2026 - 7:36

score 267 · Answer 4 · 2018-03-01 21:59:47

267

Views

measure preserving transformation question

Published on 01 Mar 2018 - 21:59

score 409 · Answer 5 · 2026-03-20 19:11:59

409

Views

Can interesting bounds to Gauss circle problem be seen/come from counting points close to a line?

Published on 20 Mar 2026 - 19:11

score 325 · Answer 6 · 2026-03-25 01:16:22

325

Views

Stationary distribution for a Markov Chain on an uncountable space

Published on 25 Mar 2026 - 1:16

score 267 · Answer 7 · 2018-03-13 22:20:14

267

Views

Proving a.e surjectivity of suggested factor map in Natural extension of Standard Borel dynamical system

Published on 13 Mar 2018 - 22:20

score 985 · Answer 8 · 2018-03-15 13:33:13

985

Views

Kac's Lemma for integrable return times

Published on 15 Mar 2018 - 13:33

score 215 · Answer 9 · 2026-03-17 18:25:24

215

Views

Limiting proportion of time spent in each state of a cyclic birth and death chain

Published on 17 Mar 2026 - 18:25

score 84 · Answer 10 · 2018-03-22 13:49:09

84

Views

Individual Ergodic Theorem, Invariance of the limit function

Published on 22 Mar 2018 - 13:49

score 221 · Answer 11 · 2026-03-25 06:03:51

221

Views

Prove the composition with measure-preserving transformation is continuous on all $L^p$

Published on 25 Mar 2026 - 6:03

score 464 · Answer 12 · 2026-03-22 14:55:06

464

Views

ergodic measure and absolutely continuous measure

Published on 22 Mar 2026 - 14:55

score 370 · Answer 13 · 2018-03-25 11:30:33

370

Views

Prove that if $\mu$ is purely atomic then $\mu=\sum_{i=1}^\infty p_i \delta_{x_i}$ s.t $\sum_{i=1}^\infty p_i=1$

Published on 25 Mar 2018 - 11:30

score 58 · Answer 14 · 2018-03-25 17:34:07

58

Views

Domino tilings of a $2 \times 10$ rectangle with notches

Published on 25 Mar 2018 - 17:34

score 113 · Answer 15 · 2018-03-28 14:10:04

113

Views

2 sided subshifts of finite type, showing something is compact

Published on 28 Mar 2018 - 14:10

List Question

Prove that $T$ is ergodic if $\mu(T^{-n}A \cap B)>0$

Does, under iteration, all strongly mixing transformations tend to spread sets out, not only in (ordinary) diameter, but also in harmonic diameter?

Density limits and sets with positive lower density

measure preserving transformation question

Can interesting bounds to Gauss circle problem be seen/come from counting points close to a line?

Stationary distribution for a Markov Chain on an uncountable space

Proving a.e surjectivity of suggested factor map in Natural extension of Standard Borel dynamical system

Kac's Lemma for integrable return times

Limiting proportion of time spent in each state of a cyclic birth and death chain

Individual Ergodic Theorem, Invariance of the limit function

Prove the composition with measure-preserving transformation is continuous on all $L^p$

ergodic measure and absolutely continuous measure

Prove that if $\mu$ is purely atomic then $\mu=\sum_{i=1}^\infty p_i \delta_{x_i}$ s.t $\sum_{i=1}^\infty p_i=1$

Domino tilings of a $2 \times 10$ rectangle with notches

2 sided subshifts of finite type, showing something is compact

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