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arXiv · 1805.09715

Ultralimits of Birkhoff averages

Maria Carvalho·Fernando Moreira
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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.

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Maria Carvalho, Fernando Moreira. 2018-05-24. Ultralimits of Birkhoff averages. https://arxiv.org/abs/1805.09715

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