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- W2949359310 abstract "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 1-dimensional averages." @default.
- W2949359310 created "2019-06-27" @default.
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- W2949359310 date "2012-06-20" @default.
- W2949359310 modified "2023-09-27" @default.
- W2949359310 title "Multivariable averaging on sparse sets" @default.
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