A Characterization of a Local Vector Valued Bollobás Theorem

A Vector-valued Random Ergodic Theorem

2. Theorem. Let £ be a reflexive B-space and let (S, 2, m) be a a-finite measure space. Let there be defined on S a strongly measurable function Ts with values in the B-space B(H) of bounded linear operators on H. Suppose that || 7\|| ^=1 for all sES. Let h be a measure-preserving transformation (m.p.t.) in (S, 2, m). Then for each XELi(S, £) there is an XELi(S, X) such that limn<„ «_1E"=i T*Th...

A Bollobás-type theorem for affine subspaces

A Characterization of Quasiconvex Vector-valued Functions

The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are K-quasiconvex with respect to a closed convex cone K in a Banach space. Our main result extends a wellknown characterization of K-quasiconvexity by means of extreme directions of the polar cone of K, obtained by Dinh The Luc in the particular case when K is a polyhedral cone generate...

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Vector ultrametric spaces and a fixed point theorem for correspondences

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.