10 citations · 31 across the 18 of their papers we have counts for
9 papers · 1 filter
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…
Recurrence and the existence of invariant measures
Manuel J. Inselmann, Benjamin D. Miller
We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, in the strong sense that if a Borel action of a locall…
On the existence of cocycle-invariant Borel probability measures
Benjamin D. Miller
We show that a natural generalization of compressibility is the sole obstruction to the existence of a cocycle-invariant Borel probability measure.
On the existence of small antichains for definable quasi-orders
Raphaël Carroy, Benjamin D. Miller, Zoltán Vidnyánszky
We generalize Kada's definable strengthening of Dilworth's characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.