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math.DS2022
A ratio ergodic theorem via tiling and uniformly syndetic markers
Benjamin D. Miller, Anush Tserunyan
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 th…
math.DS2017
Edge sliding and ergodic hyperfinite decomposition
Benjamin D. Miller, Anush Tserunyan
We use edge slidings and saturated disjoint Borel families to give a conceptually simple proof of Hjorth's theorem on cost attained: if a countable p.m.p. ergodic equivalence relat…