A non RNP Banach space E is constructed such that E∗ is separable and RNP is equivalent to PCP on the subsets of E. The problem of the equivalence of the Radon-Nikodym Property (RNP) and the Krein Milman Property (KMP) remains open for Banach spaces as well as for closed convex sets. A step forward has been made by Schachermayer’s Theorem [S]. That result states that the two properties are equi...

Data sets that characterize human activity over time through collections of timestamped events or counts are of increasing interest in application areas as humancomputer interaction, video surveillance, and Web data analysis. We propose a non-parametric Bayesian framework for modeling collections of such data. In particular, we use a Dirichlet process framework for learning a set of intensity f...

0167-8655/$ see front matter 2010 Elsevier B.V. A doi:10.1016/j.patrec.2010.11.003 q Selected as best paper at Themis2008. ⇑ Corresponding author. Fax: +39 059 2056129. E-mail addresses: [email protected] (R. unimore.it (C. Grana), [email protected] (R. C AD-HOC (Appearance Driven Human tracking with Occlusion Classification) is a complete framework for multiple people tracking...

in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

We show a general method of construction of non-porous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each non-porous Suslin subset of a topologically complete metric space contains a non-porous closed subset. We show also a suucient condition, which gives that a certain system of compact sets contains a non-porous element. Namely, if we d...

A closed subalgebra of a Banach algebra is called maximal if it is not contained in any larger proper closed subalgebra. Let G be a discrete abelian topological group and L its group-algebra, i.e. L is the Banach algebra of functions/on G with E*e<J |/(X)| < °° and multiplication defined as convolution. What are the maximal subalgebras of L? The complete answer is not known even when G is the g...

Problem B1 (20 pts). A ray , R, of E is any subset of the form R = {a+ tu | t ∈ R, t ≥ 0}, for some point, a ∈ E and some nonzero vector, u ∈ R. A subset, A ⊆ E, is unbounded iff it is not contained in any ball. Prove that every closed and unbounded convex set, A ⊆ E, contains a ray. Hint : Pick some point, c ∈ A, as the origin and consider the sphere, S(c, r) ⊆ E, of center c and radius r > 0....

Abstract. Let E be a closed set on the unit circle. We find a Blaschke-type condition, optimal in a sense of the order, on the Riesz measure of a subharmonic function v in the unit disk with a certain growth at the direction of E. In particular case when E is a finite set, and v = log |f | with an analytic function f , our result agrees with the recent one by A. Borichev, L. Golinskii and S. Ku...

A classical theorem due to R. Phelps states that if C is a weakly compact set in a Banach space E, the strongly exposing functionals form a dense subset of the dual space E. In this paper, we look at the concrete situation where C € L1pRdq is the closed convex hull of the set of random variables Y P L1pRdq having a given law ν. Using the theory of optimal transport, we show that every random va...