Displaying similar documents to “On the individual ergodic theorem for subsequences”

Convergence of the averages and finiteness of ergodic power funtions in weighted L spaces.

Pedro Ortega Salvador (1991)

Publicacions Matemàtiques

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Let (X, F, μ) be a finite measure space. Let T: X → X be a measure preserving transformation and let Af denote the average of Tf, k = 0, ..., n. Given a real positive function v on X, we prove that {Af} converges in the a.e. sense for every f in L(v dμ) if and only if inf v(Tx) > 0 a.e., and the same condition is equivalent to the finiteness of a related ergodic power function Pf for every f in L(v dμ). We apply this result to characterize, being T null-preserving, the finite...

Appendix on return-time sequences

Jean Bourgain, Harry Furstenberg, Yitzhak Katznelson, Donald S. Ornstein (1989)

Publications Mathématiques de l'IHÉS

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Almost everywhere convergence and boundedness of Cesàro-α ergodic averages in L-spaces.

Francisco J. Martín Reyes, María Dolores Sarrión Gavilán (1999)

Publicacions Matemàtiques

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Let (X, μ) be a σ-finite measure space and let τ be an ergodic invertible measure preserving transformation. We study the a.e. convergence of the Cesàro-α ergodic averages associated with τ and the boundedness of the corresponding maximal operator in the setting of L(wdμ) spaces.