Ergodic theorem, reversibility and the filling scheme

• Autorzy: Yves Derriennic
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 599-608

Daty

wydano

2010

Twórcy

autor

Yves Derriennic

• U.E.B., Mathématiques (U.M.R. CNRS 6205), Université de Brest, 6 av. Le Gorgeu, 29238 Brest, France

Identyfikatory

DOI

10.4064/cm118-2-16