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Mat. Zametki, 1970, Volume 7, Issue 1, Pages 109–115 (Mi mz6998)  

A property of compactness of families of functions harmonic with respect to a Markov process

M. G. Shur

Institute of Electronic Engineering

Abstract: Under quite general assumptions it is shown that any uniformly bounded sequence of functions, harmonic with respect to a Markov process, contains a sub-sequencewhich converges throughout phase space to some function harmonic with respect to this process. In the case of continuous processes, the demand of uniform boundedness can be replaced by the requirement of local uniform boundedness.

Full text: PDF file (551 kB)

English version:
Mathematical Notes, 1970, 7:1, 66–69

Bibliographic databases:

UDC: 519.2
Received: 16.12.1968

Citation: M. G. Shur, “A property of compactness of families of functions harmonic with respect to a Markov process”, Mat. Zametki, 7:1 (1970), 109–115; Math. Notes, 7:1 (1970), 66–69

Citation in format AMSBIB
\Bibitem{Shu70}
\by M.~G.~Shur
\paper A~property of compactness of families of functions harmonic with respect to a~Markov process
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 1
\pages 109--115
\mathnet{http://mi.mathnet.ru/mz6998}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=261694}
\zmath{https://zbmath.org/?q=an:0291.60033}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 1
\pages 66--69
\crossref{https://doi.org/10.1007/BF01093344}


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