## Bernoulli

• Bernoulli
• Volume 24, Number 1 (2018), 433-448.

### The van den Berg–Kesten–Reimer operator and inequality for infinite spaces

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 24, Number 1 (2018), 433-448.

Dates
Revised: June 2016
First available in Project Euclid: 27 July 2017

https://projecteuclid.org/euclid.bj/1501142450

Digital Object Identifier
doi:10.3150/16-BEJ883

Mathematical Reviews number (MathSciNet)
MR3706764

Zentralblatt MATH identifier
06778335

#### Citation

Arratia, Richard; Garibaldi, Skip; Hales, Alfred W. The van den Berg–Kesten–Reimer operator and inequality for infinite spaces. Bernoulli 24 (2018), no. 1, 433--448. doi:10.3150/16-BEJ883. https://projecteuclid.org/euclid.bj/1501142450

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