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Absolute Continuity and the Fine Topology

  • J. Walsh
  • W. Winkler
Chapter
  • 272 Downloads
Part of the Progress in Probability and Statistics book series (PRPR, volume 1)

Abstract

One of the basic contrasts between the classical and axiomatic theories on the one hand and their probabilistic analogues on the other is that many of the underlying hypotheses of the former are topological, and of the latter, measure-theoretical. A case in point is the regularity of excessive functions, which is assured in the classical and axiomatic settings by assuming lower semi-continuity, and in the probabilistic setting by assuming much weaker conditions such as the absolute continuity condition (hypothesis (L) of Meyer).

Keywords

Absolute Continuity Chain Condition Finite Measure Axiomatic Theory 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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References

  1. 1.
    R.M. BLUMENTHAL and R.K. GETOOR (1968). Markov Processes and Potential Theory, Academic Press, New York.Google Scholar
  2. 2.
    R. GETOOR (1975). Markov Processes: Ray Processes and Right Processes. Lecture Notes in Mathematics 440. Springer-Verlag, Berlin.Google Scholar
  3. 3.
    P.A. MEYER (1962). Functionelles multiplicatives et additive de Markov. Ann. Inst. Fourier, 12, 125–130.CrossRefGoogle Scholar
  4. 4.
    J. WALSH and P.A. MEYER (1971). Quelques applications des resolvante de Ray. Invent. Math. 14, 143–166.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1981

Authors and Affiliations

  • J. Walsh
    • 1
  • W. Winkler
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsUniversity of PittsburghPittsburghUSA

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