10 citations · 31 across the 18 of their papers we have counts for
20 papers
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…
The Feldman-Moore, Glimm-Effros, and Lusin-Novikov theorems over quotients
N. de Rancourt, B. D. Miller
We establish generalizations of the Feldman-Moore theorem, the Glimm-Effros dichotomy, and the Lusin-Novikov uniformization theorem from Polish spaces to their quotients by Borel o…
A dichotomy for countable unions of smooth Borel equivalence relations
N. de Rancourt, B. D. Miller
We show that if an equivalence relation on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of to a coun…
Bases for functions beyond the first Baire class
Raphaël Carroy, Benjamin D. Miller
We provide a finite basis for the class of Borel functions that are not in the first Baire class, as well as the class of Borel functions that are not -continuous with closed wi…
Lacunary sets for actions of tsi groups
Benjamin D. Miller
Under a mild definability assumption, we characterize the family of Borel actions of tsi Polish groups on Polish spaces that can be decomposed into countably-…
Sigma-continuity with closed witnesses
Raphaël Carroy, Benjamin D. Miller
We use variants of the dichotomy to establish a refinement of Solecki's basis theorem for the family of Baire-class one functions which are not -continuous with c…