On a theorem of Furstenberg and the structure of topologically ergodic measures

Pakula, Lewis; Sine, Robert

doi:10.1090/S0002-9939-1977-0507575-X

On a theorem of Furstenberg and the structure of topologically ergodic measures
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by Lewis Pakula and Robert Sine PDF

Proc. Amer. Math. Soc. 65 (1977), 52-56 Request permission

Abstract:

An almost everywhere convergence theorem for topologically ergodic measures stated by Furstenberg for homeomorphisms is extended to Markov operators on $C(X)$ with compact Hausdörff state space. A structure theorem for topologically ergodic measures is obtained in the compact metric case again in the more general setting of Markov operators.

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