On the expected value of vector lattice valued random variables. (English) Zbl 0621.60002

In the first part of the paper a definition is presented of the expected value of a random variable with values in an Archimedean vector lattice E. The motivation for the study of such variables are possible applications in numerous fields of probability and applied statistics such as stochastic processes, decision theory, estimation and so on. The second reason is that in a number of spaces the convergence in vector lattice (the so-called order convergence) is stronger than the topological one.
It is shown that the expected value can be correctly defined in a wide class of vector lattices including all B-lattices. In addition a convergence theorem of Beppo-Levi’s type is proved.


60A99 Foundations of probability theory
28B05 Vector-valued set functions, measures and integrals
46A40 Ordered topological linear spaces, vector lattices
44A30 Multiple integral transforms
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