# A Natural Extension of the BK Inequality

## TL;DR

This paper generalizes the van den Berg-Kesten Inequality to multiple events, providing a new tool for bounding probabilities of disjoint event occurrences in complex probability spaces.

## Contribution

It introduces an extension of the BK inequality to handle an arbitrary number of events, enhancing probabilistic bounds for event counts.

## Key findings

- Extended BK inequality to multiple events
- Provides bounds for upper tail probabilities
- Applicable to complex product spaces

## Abstract

We extend the seminal van den Berg-Kesten Inequality on disjoint occurrence of two events to a setting with arbitrarily many events, where the quantity of interest is the maximum number that occur disjointly. This provides a handy tool for bounding upper tail probabilities for event counts in a product probability space.