On the Individual Ergodic Theorem for $K$-Automorphisms

Blum, J. R.; Reich, J. I.

Ann. Probab., Tome 5 (1977) no. 6, p. 309-314 / Harvested from Project Euclid

Résumé

Let $(X, \mathscr{B}(X), P)$ be a probability space and let $T$ be a $K$-automorphism. If $T$ satisfies a Rosenblatt mixing condition of a certain kind, we show that if $\{k_n\}^\infty_{n=1}$ is an arbitrary increasing sequence of integers and $g$ belongs to a certain class of functions then $$\lim_{n\rightarrow\infty} \frac{1}{n} \sum^n_{j=1} g(T^{k_j}x) = E(g) \mathrm{a.s.}$$

Publié le : 1977-04-14
Classification: Ergodic theorem, $K$-automorphism, Rosenblatt condition, 47A35, 28A65, 60F15

@article{1176995857,
     author = {Blum, J. R. and Reich, J. I.},
     title = {On the Individual Ergodic Theorem for $K$-Automorphisms},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 309-314},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995857}
}

Blum, J. R.; Reich, J. I. On the Individual Ergodic Theorem for $K$-Automorphisms. Ann. Probab., Tome 5 (1977) no. 6, pp.  309-314. http://gdmltest.u-ga.fr/item/1176995857/