Four and a half proofs of a product-measure version of the Erdös-Ko-Rado Theorem.

Ehud Friedgut
The Weizmann Institute of Science
September 24, 2018

The EKR theorem, which is the cornerstone of extremal combinatorics, characterizes maximal intersecting families of sets. Its setting fixes a ground set of size n, and then studies the size and structure of intersecting families of subsets of fixed size k. A setting which many might consider no less natural, is considering the Boolean lattice of all subsets of {1,...,n} endowed with a product measure, and studying the structure and measure of maximal intersecting families.