Strongly mixing sequences of measure preserving transformations

Behrends, Ehrhard, and Schmeling, Jörg. "Strongly mixing sequences of measure preserving transformations." Czechoslovak Mathematical Journal 51.2 (2001): 377-385. <http://eudml.org/doc/30641>.

@article{Behrends2001,
abstract = {We call a sequence $(T_n)$ of measure preserving transformations strongly mixing if $P(T_n^\{-1\}A\cap B)$ tends to $P(A)P(B)$ for arbitrary measurable $A$, $B$. We investigate whether one can pass to a suitable subsequence $(T_\{n_k\})$ such that $\frac\{1\}\{K\} \sum _\{k=1\}^K f(T_\{n_k\}) \longrightarrow \int f \mathrm \{d\}P$ almost surely for all (or “many”) integrable $f$.},
author = {Behrends, Ehrhard, Schmeling, Jörg},
journal = {Czechoslovak Mathematical Journal},
keywords = {ergodic transformation; strongly mixing; Birkhoff ergodic theorem; Komlós theorem; ergodic transformation; strongly mixing; Birkhoff ergodic theorem; Komlós theorem},
language = {eng},
number = {2},
pages = {377-385},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Strongly mixing sequences of measure preserving transformations},
url = {http://eudml.org/doc/30641},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Behrends, Ehrhard
AU - Schmeling, Jörg
TI - Strongly mixing sequences of measure preserving transformations
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 377
EP - 385
AB - We call a sequence $(T_n)$ of measure preserving transformations strongly mixing if $P(T_n^{-1}A\cap B)$ tends to $P(A)P(B)$ for arbitrary measurable $A$, $B$. We investigate whether one can pass to a suitable subsequence $(T_{n_k})$ such that $\frac{1}{K} \sum _{k=1}^K f(T_{n_k}) \longrightarrow \int f \mathrm {d}P$ almost surely for all (or “many”) integrable $f$.
LA - eng
KW - ergodic transformation; strongly mixing; Birkhoff ergodic theorem; Komlós theorem; ergodic transformation; strongly mixing; Birkhoff ergodic theorem; Komlós theorem
UR - http://eudml.org/doc/30641
ER -