Borel Liftings of Graph Limits

@article{Orbanz2013BorelLO,
  title={Borel Liftings of Graph Limits},
  author={Peter Orbanz and Bal{\'a}zs Szegedy},
  journal={arXiv: Probability},
  year={2013}
}
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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