8 citations · 12 across the 3 of their papers we have counts for
5 papers
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…
Measurable realizations of abstract systems of congruences
Clinton T. Conley, Andrew S. Marks, Spencer T. Unger
An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congrue…
Distance from marker sequences in locally finite Borel graphs
Clinton T. Conley, Andrew S. Marks
We show that a locally finite Borel graph is nonsmooth if and only if it admits marker sequences which are "far" from every point. Our proof uses the Galvin-Prikry theorem and the…