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Laws of Chaos pp 110-126 | Cite as

Other Existence Results

  • Abraham Boyarsky
  • Paweł Góra
Part of the Probability and Its Applications book series (PA)

Abstract

In this chapter we present existence results that do not use the bounded variation technique. In particular, we shall provide a modern proof of the Folklore Theorem which established the existence of absolutely continuous invariant measure for Markov transformations. Inspired by number theoretical questions Rényi [1957] proved the first version of this theorem for piecewise onto transformations. We follow closely the development in [Adler and Flatto, 1991].

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Abraham Boyarsky
    • 1
  • Paweł Góra
    • 1
  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada

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