Probability measures in topology

The dimension problem for the product of infinite-dimensional spaces

“…As is pointed out in [29], it follows from this theorem that every c.m.i. (n), n/_-1, functor preserves the class of s.c.d, compacta.…”

“…We say that the covariant functor F preserves the class K, if for every compactum X from the class I( its image F(X) also belongs to the class K. As concerns the terminology for functors, we shall follow reviews [27,29]. Every continuous, monomorpkic functor, which preserves the intersections and is of a finite degree n, n ~ 1, will be written, for brevity, as a c.m.i.…”

Extenders for vector-valued functions

“…By [Fe,§1], measures from the set P σ (X) can be identified with σ-additive probability measures on X. This justifies the choice of notation.…”

On the openness of the idempotent barycenter map

“…Let {X α } α∈A be a family of Max-Plus convex compacta. Then the product X = α∈A X α has a natural structure of Max-Plus convexity with coordinatewise operation: The proofs of the following two theorems are analogous to the proofs of its counterparts for probability measures (Theorems 7.5 and 7.6 from [5]). Let X be a Max-Plus convex compactum.…”