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Finite probabilistic structures

Abstract Consideration of the field of events in the theory of probability gives rise to the notion of the field of events ℱ(B) consisting of a set of subsets of some set B. On the field ℱ(B), two algebraic structures are naturally defined. These are the Boolean algebra (ℱ(B)) with the operations of union, intersection and complement, and the lattice L(ℱ(B)), where the order is defined according to inclusion of the sets of ℱ(B). In this paper, we consider one more algebraic structure on ℱ(B) and the abstract variant of this structure, the so-called probabilistic structure, which is closely related to properties of the measure on ℱ(B).