Electronic Communications in Probability

Borel liftings of graph limits

Peter Orbanz and Balazs Szegedy

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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.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 65, 4 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]

graph limits random graphs

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Orbanz, Peter; Szegedy, Balazs. Borel liftings of graph limits. Electron. Commun. Probab. 21 (2016), paper no. 65, 4 pp. doi:10.1214/16-ECP14. https://projecteuclid.org/euclid.ecp/1473854581

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