Open Access
April, 1977 On the Individual Ergodic Theorem for $K$-Automorphisms
J. R. Blum, J. I. Reich
Ann. Probab. 5(2): 309-314 (April, 1977). DOI: 10.1214/aop/1176995857


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 $$\lim_{n\rightarrow\infty} \frac{1}{n} \sum^n_{j=1} g(T^{k_j}x) = E(g) \mathrm{a.s.}$$


Download Citation

J. R. Blum. J. I. Reich. "On the Individual Ergodic Theorem for $K$-Automorphisms." Ann. Probab. 5 (2) 309 - 314, April, 1977.


Published: April, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0368.28025
MathSciNet: MR430207
Digital Object Identifier: 10.1214/aop/1176995857

Primary: 47A35
Secondary: 28A65 , 60F15

Keywords: $K$-automorphism , ergodic theorem , Rosenblatt condition

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 2 • April, 1977
Back to Top