Mean ergodic theorem and multiplicative cocycles

  • Choe, Geon H. (Department of Mathematics, Korea Advanced Institute of Science and Technology)
  • 발행 : 1996.02.01

초록

Let $(X, B, \mu)$ be a probability space. Then we say $\tau : X \to X$ is a measure-preserving transformation if $\mu(\tau^{-1} E) = \mu(E)$. and we call it an ergodic transformation if $\mu(\tau^{-1}E\DeltaE) = 0$ for a measurable subset E implies $\mu(E) = 0$. An equivalent definition is that constant functions are the only $\tau$-invariant functions.

키워드