Join-Semilattices of Integrable Set-Valued Martingales

Coenraad C. A. Labuschagne

Abstract

We derive order properties of set-valued (reversed) martingales. We show that the space of set-valued integrable (reversed) martingales with respect to a given filtration is a join-semilattice. Similar results are obtained for spaces of set-valued integrably bounded convergent martingales.