## Bernoulli

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

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

Richard Arratia, Skip Garibaldi, and Alfred W. Hales

#### 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**

Received: December 2015

Revised: June 2016

First available in Project Euclid: 27 July 2017

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.3150/16-BEJ883

**Mathematical Reviews number (MathSciNet)**

MR3706764

**Zentralblatt MATH identifier**

06778335

**Keywords**

BKR inequality projective set van den Berg–Kesten–Reimer

#### 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