Valuations: from convex geometry to function spaces

23/02/2018, 14:00 - 15:00 in MAP/0G/018

Tradacete, Pedro (Universidad Carlos III de Madrid)

Abstract:

A valuation is a function V, defined on a given class of sets, which satisfies that for every A,B

V (A ∪ B) + V (A ∩ B)=V (A) + V (B)

whenever both union and intersection of A and B also belong to the class. Valuations are a generalization of the notion of measure, and have become a relevant area of study in convex geometry. I will present some recent results on the structure and representation of valuations on star shaped bodies. These will be based on techniques from measure theory and functional analysis.