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math.DS2023
Moving Averages
Terrence Adams, Joseph Rosenblatt
We consider the convergence of moving averages in the general setting of ergodic theory or stationary ergodic processes. We characterize when there is universal convergence of movi…
math.DS2014
Entropy and the Uniform Mean Ergodic Theorem for a Family of Sets
Terrence M. Adams, Andrew B. Nobel
We define a notion of entropy for an infinite family of measurable sets in a probability space. We show that the mean ergodic theorem holds uniformly for $\mathcal{C}…