Ultralimits of Birkhoff averages

Abstract

Given a compact metric space $X$ and a probability measure in the $\sigma -$algebra of Borel subsets of $X$, we will establish a dominated convergence theorem for ultralimits of sequences of integrable maps and apply it to deduce a non-standard ergodic-like theorem for any probability measure.

References in corpus (1)

• Takens' last problem and existence of non-trivial wandering domains

Cited by in corpus (1)

• A Kingman-like Theorem