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Results tagged with ergodic-theory
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user 8382
Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
25
votes
6
answers
6k
views
Proof of Krylov-Bogoliubov theorem
Where can I find a proof (in English) of the Krylov-Bogoliubov theorem, which states if $X$ is a compact metric space and $T\colon X \to X$ is continuous, then there is a $T$-invariant Borel probabili …
- 897
17
votes
3
answers
2k
views
Applications of and motivation for von Neumann's mean ergodic theorem
I stated von Neumann's mean ergodic theorem (VNMET) in a talk recently and someone in the audience asked what it was good for. The only application I knew of VNMET was to prove Birkhoff's ergodic theo …
- 897
2
votes
1
answer
1k
views
Shift invariant measures that are(n't) convex combinations of ergodic measures
Let $X=2^\omega = \lbrace 0,1 \rbrace^{\mathbb{N}}$ and $T\colon X \to X$ the (left) shift map. The space $\mathcal{M}$ of $T$-invariant Borel probability measures is convex with $\mathcal{M}^e$, the …
- 897