Borel Liftings of Graph Limits

  title={Borel Liftings of Graph Limits},
  author={Peter Orbanz and Bal{\'a}zs Szegedy},
  journal={arXiv: Probability},
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. 
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A general theorem on selectors
  • Bulletin de l’Academie Polonaise des Sciences; Serie des Sciences Mathèmatiques, Astronomiques et Physiques,
  • 1965