A THEOREM DESCRIBING THE STRUCTURE OF SET MAPPINGS BETWEEN MEASURE ALGEBRAS
Ali A. Mehemmed · Demonstratio Mathematica · 1999
The subject of this paper is the problem of describing the structure of set mappings h between two measure algebras (Ai, m) and (A2, ^2) effectively.We shall use disjoint partitions of the cr-algebras Aj and A2, and we shall assume that the homomorphism h : Ai -» A2 is continuous.We shall construct a pairwise disjoint sequence (An) in the second cr-algebra A2 which covers the homomorphic image of the whole space Xi and for n € N we construct a partition {¿?in) ¿?2n> • • •) Eknn) of the first space X\ so that the set mapping hin : Ai (Ein) -• A2 (An D h(Ein)) is a cr-homomorphism.