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Coupling of the GB set property for ergodic averages

Authors:	Michel Weber

Affiliation:	(1) Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7, rue René Descartes, 67084 Strasbourg Cedex, France

Abstract:	Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL²() such that $I(A) = int_0^{diam(A)} {sqrt {log N(A,u)} du< infty }$ , whereA=sup{\|\|sȒt\|\|₂,s, tA} andN(A, u) is the smallest number ofL²()-open balls of radiusu, centered inA, enough to coverA. Let $C(A) = left{ {tfrac{1}{n}Sigma _{i - 0}^{n - 1} f circ T^i ,n geqslant 1,f in A} right}$ . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL²().

Keywords:	Ergodic dynamical system coupling Gaussian processes GB sets
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