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

Authors: Lewis Pakula and Robert Sine
Journal: Proc. Amer. Math. Soc. 65 (1977), 52-56
MSC: Primary 28A65; Secondary 60J05
MathSciNet review: 0507575
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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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Keywords: Topologically ergodic measures, Choquet representation
Article copyright: © Copyright 1977 American Mathematical Society