Ergodic theorem, reversibility and the filling scheme

Yves Derriennic. "Ergodic theorem, reversibility and the filling scheme." Colloquium Mathematicae 118.2 (2010): 599-608. <http://eudml.org/doc/284166>.

@article{YvesDerriennic2010,
abstract = {The aim of this short note is to present in terse style the meaning and consequences of the "filling scheme" approach for a probability measure preserving transformation. A cohomological equation encapsulates the argument. We complete and simplify Woś' study (1986) of the reversibility of the ergodic limits when integrability is not assumed. We give short and unified proofs of well known results about the behaviour of ergodic averages, like Kesten's lemma (1975). The strikingly simple proof of the ergodic theorem in one dimension given by Neveu (1979), without any maximal inequality nor clever combinatorics, followed this approach and was the starting point of the present study.},
author = {Yves Derriennic},
journal = {Colloquium Mathematicae},
keywords = {Birkhoff's theorem; filling scheme},
language = {eng},
number = {2},
pages = {599-608},
title = {Ergodic theorem, reversibility and the filling scheme},
url = {http://eudml.org/doc/284166},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Yves Derriennic
TI - Ergodic theorem, reversibility and the filling scheme
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 599
EP - 608
AB - The aim of this short note is to present in terse style the meaning and consequences of the "filling scheme" approach for a probability measure preserving transformation. A cohomological equation encapsulates the argument. We complete and simplify Woś' study (1986) of the reversibility of the ergodic limits when integrability is not assumed. We give short and unified proofs of well known results about the behaviour of ergodic averages, like Kesten's lemma (1975). The strikingly simple proof of the ergodic theorem in one dimension given by Neveu (1979), without any maximal inequality nor clever combinatorics, followed this approach and was the starting point of the present study.
LA - eng
KW - Birkhoff's theorem; filling scheme
UR - http://eudml.org/doc/284166
ER -