Random covering sets in metric space with exponentially mixing property

摘要

Let {B(xi(n), r(n))}(n >= 1) be a sequence of random balls whose centers {xi(n)}(n >= 1) is a stationary process, and {r(n)}(n >= 1) is a sequence of positive numbers decreasing to 0. Our object is the random covering set E = lim sup(n ->infinity) B(xi(n), r(n)), that is, the points covered by B(xi(n), r(n)) infinitely often. The sizes of E are investigated from the viewpoint of measure, dimension and topology.

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