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Topological dynamics of transformations induced on the space of probability measures

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Abstract

LetT be a continuous transformation of a compact metric spaceX. T induces in a natural way a transformationT M on the spaceM (X) of probability measures onX, and a transformationT K on the spaceK (X) of closed subsets ofX. This note investigates which of the topological properties ofT∶X→X (like distality, transitivity, mixing property etc. ...) are “inherited” byT M∶M (X)→M (X) andT K∶K (X)→K (X).

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Authors and Affiliations

  1. I. Lehrkanzel für Mathematik der Universität Salzburg, Porschestraße 1/I, A-5020, Salzburg, Austria

    Walter Bauer

  2. Math. Institut der Universität, Strudlhofgasse 4, A-1090, Wien, Austria

    Karl Sigmund

Authors
  1. Walter Bauer
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  2. Karl Sigmund
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Dedicated to Prof. N. Hofreiter on his seventieth birthday

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Bauer, W., Sigmund, K. Topological dynamics of transformations induced on the space of probability measures. Monatshefte fü Mathematik 79, 81–92 (1975). https://doi.org/10.1007/BF01585664

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  • DOI: https://doi.org/10.1007/BF01585664

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