Infinite Divisibility of Random Objects in Locally Compact Positive Convex Cones

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

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 ...

On infinite divisibility and embedding of probability measures on a locally compact Abelian group

In the present note the authors supplement significant properties of infinitely divisible and embeddable probability measures on a locally compact Abelian group G. There are at least two versions of infinite divisibility appearing in the literature which deserve special attention, and the problem of embedding those measures leads directly to the study of continuous convolution semigroups on G. ...

Infinite Locally Random Graphs

Motivated by copying models of the web graph, Bonato and Janssen [3] introduced the following simple construction: given a graph G, for each vertex x and each subset X of its closed neighbourhood, add a new vertex y whose neighbours are exactly X. Iterating this construction yields a limit graph ↑G. Bonato and Janssen claimed that the limit graph is independent of G, and it is known as the infi...