Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 65, 4 pp.
Borel liftings of graph limits
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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 05C80: Random graphs [See also 60B20]
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