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Jul 29, 2021 at 23:32 history became hot network question
Jul 29, 2021 at 20:16 answer added Ronnie Pavlov timeline score: 4
Jul 29, 2021 at 19:58 history edited YCor CC BY-SA 4.0
removed capitals from title
S Jul 29, 2021 at 18:50 vote accept Julian Hölz
S Jul 29, 2021 at 18:50 vote accept Julian Hölz
S Jul 29, 2021 at 18:50
Jul 29, 2021 at 16:49 vote accept Julian Hölz
S Jul 29, 2021 at 18:50
Jul 29, 2021 at 16:29 history edited Julian Hölz CC BY-SA 4.0
Exclude trivial cases from the question
Jul 29, 2021 at 16:20 comment added Julian Hölz Thank you. This seemed to have to have crossed my mind only after posting the question. Perhaps we could modify the question to the following: Under which conditions is the set of ergodic measures $\mu$ of $\varphi$ that have a support $\mathrm{supp}(\mu)$ that contains at least 2 elements countable.
Jul 29, 2021 at 16:08 comment added Jochen Glueck Welcome (and Servus :-) ) to MathOverflow! In addition to the answers already given, let's note that if $\varphi$ is simply the identity mapping, then the invariant ergodic measures are precisely the Dirac point measures - so their cardinality equals the cardinality of $X$.
Jul 29, 2021 at 15:57 answer added Vaughn Climenhaga timeline score: 8
Jul 29, 2021 at 15:57 answer added Yuval Peres timeline score: 7
Jul 29, 2021 at 15:35 review First posts
Jul 29, 2021 at 15:54
Jul 29, 2021 at 15:30 history asked Julian Hölz CC BY-SA 4.0