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 Pvalued functions and operator valued measure θ : R → L(P, Q), where R

is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone

and (Q, W) is a locally convex complete lattice cone.