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arXiv · 2208.06463

A ratio ergodic theorem via tiling and uniformly syndetic markers

Benjamin D. Miller·Anush Tserunyan
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Abstract

We prove a purely Borel/measureless version of Dowker's ratio ergodic theorem, from which we derive a strengthening of Dowker's original theorem with a precise identification of the limit of local ergodic ratios. This is done by implementing the pointwise tiling idea of [Tse18] in the more complex setting of continuum-to-one Borel transformations. Along the way, we establish a vanishing markers lemma for these transformations, which generalizes its well-known counterpart for invertible transformations.

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Benjamin D. Miller, Anush Tserunyan. 2025-09-19. A ratio ergodic theorem via tiling and uniformly syndetic markers. https://doi.org/10.1515/9783111435503-004

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