Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 198-204
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L. A. Grigorenko. On the $\sigma$-algebra of symmetrical events for a countable Markov chain. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 198-204. http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a20/
@article{TVP_1979_24_1_a20,
author = {L. A. Grigorenko},
title = {On the $\sigma$-algebra of symmetrical events for a countable {Markov} chain},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {198--204},
year = {1979},
volume = {24},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a20/}
}
TY - JOUR
AU - L. A. Grigorenko
TI - On the $\sigma$-algebra of symmetrical events for a countable Markov chain
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1979
SP - 198
EP - 204
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a20/
LA - ru
ID - TVP_1979_24_1_a20
ER -
%0 Journal Article
%A L. A. Grigorenko
%T On the $\sigma$-algebra of symmetrical events for a countable Markov chain
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1979
%P 198-204
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a20/
%G ru
%F TVP_1979_24_1_a20
It is proved that the $\sigma$-algebra of symmetrical events for a countable Markov chain $\{x_n, n\ge 1\}$ coincides a. s. with $T(\sigma_1\bigcap\sigma_2)$, where $T$ is a left shift and $\sigma_i=\sigma(x_i)$, $i=1,2$.
