Abstract
In this paper, the Hausdorff dimensions of level sets described by two kinds of moving averages are determined. The dissimilar results complement the work of Pfaffelhuber [Moving shift averages for ergodic transformation, Metrika22 (1975) 97–101] and del Junco and Steele [Moving averages of ergodic processes, Metrika24 (1977) 35–43], and reveal simultaneously that the two moving averages are of different convergence processes in the ergodic theory.
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