Measurable one-ended spanning trees
arXiv:2509.15000
Abstract
We show that a one-ended, locally finite, measurable graph on a standard probability space admits a measurable one-ended spanning subtree if and only if it is measure-hyperfinite. This answers a question posed by Bowen, Poulin, and Zomback and extends recent results of Timár and Conley, Gaboriau, Marks, and Tucker-Drob.