科研之友
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摘要
Nonstandard ergodic averages can be defined for a measure-preserving action of a group on a probability space, as a natural extension of classical (nonstandard) ergodic averages. We extend the one-dimensional theory, obtaining L-1 pointwise ergodic theorems for several kinds of nonstandard sparse group averages, with a special focus on the group Z(d). Namely, we extend results for sparse block averages and sparse random averages to their analogues on virtually nilpotent groups, and extend Christ's result for sparse deterministic sequences to its analogue on Z(d). The second and third results have two nontrivial variants on Z(d): a "native" d-dimensional average and a "product" average from the one-dimensional averages.
- 出版日期2014-6
