Borel Liftings of Graph Limits
Abstract
The cut pseudometric 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 Borelmeasurable mapping which maps each equivalence class to one of its elements.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 arXiv:
 arXiv:1312.7351
 Bibcode:
 2013arXiv1312.7351O
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics