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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