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On limit theorems and category for dynamical systems. (English) Zbl 0735.60025

Summary: Let a probability space and a \(1-1\) bimeasurable and measure preserving transformation be given. For a measurable function \(f\), the process \((f\circ T^ i)\) is strictly stationary. Let us consider \(L^ p\) spaces of functions \(f\) and their subsets which are determined by the limit behavior of the process \((f\circ T^ i)\) from the point of view of the central limit problem and the speed of convergence in the ergodic theorem. It is shown that the set of processes (functions \(f\)) with highly irregular behavior is of second category.

MSC:

60F05 Central limit and other weak theorems
60F15 Strong limit theorems
28D05 Measure-preserving transformations
60G10 Stationary stochastic processes
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