Precalibre pairs of measure algebras

We consider Radon measures μ and pairs (κ,λ) of cardinals such that among every κ many positive measure sets there are λ many whose intersection is nonempty. Such families are connected with the cardinal invariants of the ideal of μ-null sets and have found applications in various subjects of topological measure theory. We survey many of such connections and applications and give some new ones. In particular we show that it is consistent to have a Corson compact space carrying a Radon measure of type c>ℵ1 and we partially answer a question of Haydon about measure precalibres.