A proof of the union-closed sets conjecture

Abstract

We provide a proof of the union-closed sets conjecture, by means of a suitable refinement of the breakthrough entropy-approach introduced by Gilmer. The novelty here is to consider a convex combination of $A$ and $A\cup B$, where $A,B$ are independent samples from the uniform distribution over a union-closed family.

There is a mistake in the proof of Proposition 1.2, at the end of page 4