Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

Author(s):

D. Ayaseh , A. Ranjbari

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 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.
Keywords:

Locally convex cones , Egoroff Theorem , Operator valued measure

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:12 Issue: 2, Nov 2017
Pages:
117 to 125
https://www.magiran.com/p1746016