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A Remark on the Continuity of the Dual Process

Published online by Cambridge University Press:  22 January 2016

Mamoru Kanda
Mamoru Kanda*
Affiliation:
Nagoya University
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Let S be a locally compact (not compact) Hausdorff space satisfying the second axiom of countability and let ℬ be the σ field of all Borel subsets of S and let A be the σ-field of all the subsets of S which, for each finite measure μ defined on (S, A), are in the completed σ field of ℬ relative to μ. We denote by C0 the Banach space of continuous functions vanishing at infinity with the uniform norm and Bk the space of bounded A-measurable functions with compact support in S.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 287 - 295
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Hunt, G.A.: Markoff processes and potentials, 3 Illinois J. Math. (1958), 151–213.Google Scholar
[2] Kanda, M.: Regular points and Green functions in Markov processes, Soc. Japan, Vol. 19 No. 1, (1967), 46–69.Google Scholar
[3] Kunita, H. and Watanabe, T.: Markov processes and Martin boundaries, Illinois J. Math., 9 (1965), 485–526.Google Scholar
[4] Meyer, P.A.: Semi-groupes en dualité, séminaire Brelot-Choquet-Deny (théorie du potentiel) (1960–1961).Google Scholar
[5] Watanabe, S.: On discontinuous additive functionals and Lévy measures of a Markov process, Japanese J. Math. 36 (1964), 53–70.Google Scholar