Geodesic
On the preservation of statistical properties for subsequences of random sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 715-724 
D. B. Sten'kin. On the preservation of statistical properties for subsequences of random sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 715-724. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a8/
@article{TVP_1983_28_4_a8,
     author = {D. B. Sten'kin},
     title = {On the preservation of statistical properties for subsequences of random sequences},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {715--724},
     year = {1983},
     volume = {28},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X$ be a one-sided sequence space and $\mathbf P$ be a probability measure on $X$ invariant under the shift transformation $T$ and such that the coordinates $x_i$ of $x\in X$ are weakly dependent. It is well-known that $\mathbf P$-almost every point $x\in X$ is $\mathbf P$-normal, i. e. for any sufficiently good $A\subset X$ $$ \lim_{n\to\infty}n^{-1}\operatorname{card}\{i:T^ix\in A,\ i\le n\}=\mathbf P(A). $$ We find conditions on the integer-valued sequence $\tau=(\tau_0,\tau_1,\dots)$ under which the normality of a point $x=(x_0,x_1,\dots)\in X$ s X implies that of the point $x'=(x_{\tau_0},x_{\tau_1},\dots)$.