This article is cited in 1 paper

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.

UDC: 519.2

Received: 16.12.1968

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

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