Open Access
2016 Borel liftings of graph limits
Peter Orbanz, Balazs Szegedy
Electron. Commun. Probab. 21: 1-4 (2016). DOI: 10.1214/16-ECP14


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 the equivalence relation admits a Borel lifting: There exists a Borel-measurable mapping that maps each equivalence class to one of its elements. The result yields a general framework for proving measurability properties on the space of graph limits. We give several examples, including Borel-measurability of the set of isomorphism classes of random-free graphons.


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Peter Orbanz. Balazs Szegedy. "Borel liftings of graph limits." Electron. Commun. Probab. 21 1 - 4, 2016.


Received: 15 July 2016; Accepted: 5 August 2016; Published: 2016
First available in Project Euclid: 14 September 2016

zbMATH: 1346.05274
MathSciNet: MR3548777
Digital Object Identifier: 10.1214/16-ECP14

Primary: 05C80

Keywords: Graph limits , Random graphs

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