Continuous valuations on convex sets and Monge-Ampere operators

Finitely additive measures on convex convex sets are called valuations. Valuations continuous in
the Hausdorff metric are of special interest and have been studied in convexity for a long time.
In this talk I will present a non-traditional method of constructing continuous valuations using
various Monge-Ampere (MA) operators, namely the classical complex MA operator and introduced by
the speaker quaternionic MA operators (if time permits, I will briefly discuss also octonionic case).
In several aspects analytic properties of the latter are very similar to the properties of the former,
but the geometric meaning is different. The construction of the quaternionic MA operator uses
non-commutative determinants.