Matematičeskie zametki, Tome 7 (1970) no. 1, pp. 109-115
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M. G. Shur. A property of compactness of families of functions harmonic with respect to a Markov process. Matematičeskie zametki, Tome 7 (1970) no. 1, pp. 109-115. http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a11/
@article{MZM_1970_7_1_a11,
author = {M. G. Shur},
title = {A~property of compactness of families of functions harmonic with respect to {a~Markov} process},
journal = {Matemati\v{c}eskie zametki},
pages = {109--115},
year = {1970},
volume = {7},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a11/}
}
TY - JOUR
AU - M. G. Shur
TI - A property of compactness of families of functions harmonic with respect to a Markov process
JO - Matematičeskie zametki
PY - 1970
SP - 109
EP - 115
VL - 7
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a11/
LA - ru
ID - MZM_1970_7_1_a11
ER -
%0 Journal Article
%A M. G. Shur
%T A property of compactness of families of functions harmonic with respect to a Markov process
%J Matematičeskie zametki
%D 1970
%P 109-115
%V 7
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a11/
%G ru
%F MZM_1970_7_1_a11
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.
