Geometric Tomography of Convex Cones

Geometric Tomography of Convex Cones

The parallel X-ray of a convex set K ⊂ R in a direction u is the function which associates to each line l parallel to u the length of K ∩ l. The problem of nding a set of directions such that the corresponding X-rays distinguish any two convex bodies has been widely studied in geometric tomography. In this paper we are interested in the restriction of this problem to convex cones, and we are mo...

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.

Rough convex cones and rough convex fuzzy cones

Based on the equivalence relation on a linear space, in this paper we introduce the definition of rough convex cones and rough convex fuzzy cones and discuss some of the fundamental properties of such rough convex cones.

Some Results on Boundedness in Locally 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 ...