The smash sum is the unique sum of open sets satisfying a natural list of axioms

Abstract

A sum of open sets is a map taking two bounded open sets $A,B$ and producing a new open set $A\oplus B$. We prove that, up to sets of measure zero, there is only one such sum satisfying a natural list of axioms. It is the scaling limit of the Diaconis-Fulton smash sum.

arXiv comment25 pages