On Weak Separation of Convex Sets and on $\alpha$-Ubiquitous Sets.

On bD-Sets and Associated Separation Axioms

Separation of Convex Sets

A line L separates a set A from a collection S of plane sets if A is contained in one of the closed half-planes defined by L, while every set in S is contained in the complementary closed half-plane. Let f(n) be the largest integer such that for any collection F of n closed disks in the plane with pairwise disjoint interiors, there is a line that separates a disk in F from a subcollection of F ...

On aggregation sets and lower-convex sets

It has been a challenge to characterize the set of all possible sums of random variables with given marginal distributions, referred to as an aggregation set in this paper. We study the aggregation set via its connection to the corresponding lower-convex set, which is the set of all sums of random variables that are smaller than the respective marginal distributions in convex order. Theoretical...

On the weak closure of convex sets of Probability measures

We prove that a closed, geodesically convex subset C of P 2 (R) is closed with respect to weak convergence in P 2 (R). This means that if (μn) ⊂ C is such that μn ⇀ μ in duality with continuous bounded functions and supn ∫ |x|dμn <∞, then μ ∈ C as well.

on bd-sets and associated separation axioms