Conditional expectation and martingales of random sets

摘要: Abstract The aim of this paper is to present a self-contained introduction the theory martingales random sets (also called `set-valued martingales’ or `multivalued martingales'). For purpose, we first method for constructing integral and conditional expectation with compact convex values in R d . This was used by Debreu set-valued integral. It based on approximation simple sets, i.e., assuming only finite number values. allows us recover classical properties real-valued variables deduce new applications, such as an extension Brunn-Minkowski inequality. Afterwards, multivalued are introduced, well submartingales supermartingales. We prove several convergence results, give examples applications. Further, strong laws large numbers sequences independent briefly examined. Another approach defining also sketched, existence theorem martingale selections stated. last section devoted definition non sets. Finally, short annex, criterion set be single-valued.