Volný, Dalibor On limit theorems and category for dynamical systems. (English) Zbl 0735.60025 Yokohama Math. J. 38, No. 1, 29-35 (1990). 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. Cited in 5 Documents MSC: 60F05 Central limit and other weak theorems 60F15 Strong limit theorems 28D05 Measure-preserving transformations 60G10 Stationary stochastic processes Keywords:measure preserving transformation; central limit problem; ergodic theorem; central limit problem for strictly stationary processes; speed of convergence PDFBibTeX XMLCite \textit{D. Volný}, Yokohama Math. J. 38, No. 1, 29--35 (1990; Zbl 0735.60025)