Rosenthal Families

A collection of infinite subsets of the natural numbers is a Rosenthal family if it can replace the family of all infinite subsets in a classical Lemma by Rosenthal concerning sequences of measures on pairwise disjoint sets. In this talk we will show that every ultrafilter is a Rosenthal family and that the minimal size of a Rosenthal family is the reaping number. We will also show some connections to functional analysis.