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On the existence of a σ-finite invariant measure under a generalized Harris condition

Part of the Lecture Notes in Mathematics book series (LNM,volume 160)

Abstract

A Markov transition probability function was shown by Harris [3] to admit a σ-finite invariant measure, under a certain probabilistic recurrence condition which was later given an essentially equivalent measure-theoretic form (see [2], [4], [5], and [8]). The latter includes the assumption that if T is the L operator induced by the system, then the L norm of T is one. The present paper weakens this assumption replacing it by: lim inf Tn h < ∞ a.e.

Keywords

  • Invariant Measure
  • Countable Union
  • Positive Linear Operator
  • Small Function
  • Markov Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research supported by the National Science Foundation, Grants GP 8781 and GP 7693.

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References

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© 1970 Springer-Verleg

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Ornstein, D.S., Sucheston, L. (1970). On the existence of a σ-finite invariant measure under a generalized Harris condition. In: Contributions to Ergodic Theory and Probability. Lecture Notes in Mathematics, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060655

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  • DOI: https://doi.org/10.1007/BFb0060655

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05188-6

  • Online ISBN: 978-3-540-36371-2

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