Open Access
February 2018 The van den Berg–Kesten–Reimer operator and inequality for infinite spaces
Richard Arratia, Skip Garibaldi, Alfred W. Hales
Bernoulli 24(1): 433-448 (February 2018). DOI: 10.3150/16-BEJ883


We remove the hypothesis “$S$ is finite” from the BKR inequality for product measures on $S^{d}$, which raises some issues related to descriptive set theory. We also discuss the extension of the BKR operator and inequality, from 2 events to 2 or more events, and we remove, in one sense, the hypothesis that $d$ be finite.


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Richard Arratia. Skip Garibaldi. Alfred W. Hales. "The van den Berg–Kesten–Reimer operator and inequality for infinite spaces." Bernoulli 24 (1) 433 - 448, February 2018.


Received: 1 December 2015; Revised: 1 June 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778335
MathSciNet: MR3706764
Digital Object Identifier: 10.3150/16-BEJ883

Keywords: BKR inequality , projective set , van den Berg–Kesten–Reimer

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 1 • February 2018
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