Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

Abstract. In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for P- valued functions and operator valued measure : R ! L(P,Q), where R is a -ring of subsets of X 6= ;, (P, V) is a quasi-full locally convex cone and (Q,W) is a locally convex complete lattice cone.