Motivated by original Skorokhod's ideas, a new topology has been deened on the space P(X) of tight probability distributions on a topological space (X;). The only topological assumption imposed on (X;) is that some countable family of continuous functions separates points of X. This new sequential topology, deened by means of a variant of the a.s. Skorokhod representation, is quite operational ...

We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform-weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity...

The category of framed correspondences Fr∗(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [Voe]. Based on the theory, framed motives are introduced and studied in [GP1]. The aim of this paper is to prove the following results stated in [GP1, 9.3]: for any k-smooth scheme X and any n > 1 the map of simplicial pointed sheaves (−,A⌋Gm) + → T n induces ...

(A) We consider measure preserving actions of an infinite, countable (discrete) group Γ on non-atomic standard measure spaces (X,μ), i.e., standard Borel spaces equipped with a non-atomic probability Borel measure. (All such measure spaces are isomorphic to ([0, 1], λ), where λ is Lebesgue measure.) We denote by A(Γ, X, μ) the space of such actions. If a ∈ A(Γ, X, μ) and γ ∈ Γ, we denote by γ(x...

The first part of the paper deals with general features of weak star convergence from a topological point of view. We present basic facts about weak and weak star topologies, dual spaces and representations of linear functionals as Radon measures. A special attention is payed to finitely additive measures and some results regarding the Baire sets. We prove that in a wide class of topological sp...

is a vector space isomorphism of V" onto T(m). The tangent bundle 3(Af) of the manifold M consists of the ordered pairs (m, v) where mEM and vE T(m). Therefore, as a point set only, 3(Af) is M X V". We shall assume that the reader is familiar with the fibre space topology which is customarily assigned to 3(M). (For a description of this topology and the facts concerning fibre bundles which we s...