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An existence theorem for probability measures invariant under a Markov kernel

  • Wolfgang Adamski
Article

Abstract

LetP be a Markov kernel defined on a measurable space (X,A). A probability measure μ onA is said to beP-invariant if μ(A=∫P(x,A)dμ(x) for allAAA. In this note we prove a criterion for the existence ofP-invariant probabilities which is, in particular, a substantial generalization of a classical theorem due to Oxtoby and Ulam ([5]). As another consequence of our main result, it is shown that every pseudocompact topological space admits aP-invariant Baire probability measure for any Feller kernelP.

Keywords

Probability Measure Existence Theorem Vector Lattice Markov Operator Markov Kernel 
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.

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Copyright information

© Springer 1990

Authors and Affiliations

  • Wolfgang Adamski
    • 1
  1. 1.Mathematisches Institut derUniversität MünchenMünchen 2Germany

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