Convergence of the averages and finiteness of ergodic power funtions in weighted L1 spaces.

Título inglés Convergence of the averages and finiteness of ergodic power funtions in weighted L1 spaces.
Título español Convergencia de las medias y finitud de las funciones de potencias ergódicas en espacios L1 ponderados.
Autor/es Ortega Salvador, Pedro
Organización Dep. Estadist. Econometr. Fac. Econ. Univ. Málaga, Málaga, España
Revista 0214-1493
Publicación 1991, 35 (2): 465-473, 17 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Let (X, F, μ) be a finite measure space. Let T: X → X be a measure preserving transformation and let Anf denote the average of Tkf, k = 0, ..., n. Given a real positive function v on X, we prove that {Anf} converges in the a.e. sense for every f in L1(v dμ) if and only if infi ≥ 0 v(Tix) > 0 a.e., and the same condition is equivalent to the finiteness of a related ergodic power function Prf for every f in L1(v dμ). We apply this result to characterize, being T null-preserving, the finite measures ν for which the sequence {Anf} converges a.e. for every f Î L1(dν) and to prove that uniform boundedness of the averages in L1 is sufficient for finiteness a.e. of Pr.
Código MathReviews MR1201568
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