Borel Liftings of Graph Limits
Probability
2013-12-31 v1 Combinatorics
Abstract
The cut pseudo-metric on the space of graph limits induces an equivalence relation. The quotient space obtained by collapsing each equivalence class to a point is a metric space with appealing analytic properties. We show that the equivalence relation admits a Borel lifting: There exists a Borel-measurable mapping which maps each equivalence class to one of its elements.
Keywords
Cite
@article{arxiv.1312.7351,
title = {Borel Liftings of Graph Limits},
author = {Peter Orbanz and Balazs Szegedy},
journal= {arXiv preprint arXiv:1312.7351},
year = {2013}
}