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math.DS2024
Uncountable Hyperfiniteness and The Random Ratio Ergodic Theorem
Nachi Avraham-Re'em, George Peterzil
We show that the orbit equivalence relation of a free action of a locally compact group is hyperfinite (à la Connes-Feldman-Weiss) precisely when it is 'hypercompact'. This implies…
math.DS2024
The Hopf decomposition of locally compact group actions
Nachi Avraham-Re'em, George Peterzil
We develop a unified approach to the classical Hopf Decomposition (also known as the conservative--dissipative decomposition) for actions of locally compact second countable groups…
math.CO2024
Set Systems with Covering Properties and Low VC-Dimension
George Peterzil, Johanna Steinmeyer
Given natural numbers , we ask: what is the minimal VC-dimension of a family of -subsets of that covers all -subsets of ? We first s…