On measures of size for convex cones

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

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 ...

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Some Results on Boundedness in Locally Convex Cones

Bishop-Phelps type Theorem for Normed Cones

In this paper the notion of  support points of convex sets  in  normed cones is introduced and it is shown that in a  continuous normed cone, under the appropriate conditions, the set of support points of a  bounded Scott-closed convex set is nonempty. We also present a Bishop-Phelps type Theorem for normed cones.

A cone theoretic Krein-Milman theorem in semitopological cones

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.