8 citations · 14 across the 5 of their papers we have counts for
10 papers
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…
Measure reducibility of countable Borel equivalence relations
Clinton T. Conley, Benjamin D. Miller
We show that every basis for the countable Borel equivalence relations strictly above under measure reducibility is uncountable, thereby ruling out natural generaliz…
Measurable perfect matchings for acyclic locally countable Borel graphs
Clinton T. Conley, Benjamin D. Miller
We characterize the structural impediments to the existence of Borel perfect matchings for acyclic locally countable Borel graphs admitting a Borel selection of finitely many ends…
Incomparable actions of free groups
Clinton T. Conley, Benjamin D. Miller
Suppose that is a Polish space, is a countable Borel equivalence relation on , and is an -invariant Borel probability measure on . We consider the circumstance…