We study topological properties of random metric spaces which arise by Λ-coalescents. These are stochastic processes, which start with an infinite number of lines and evolve through multiple mergers in an exchangeable setting. We show that the resulting Λ-coalescent measure tree is compact iff the Λ-coalescent comes down from infinity, i.e. only consists of finitely many lines at any positive t...

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...

We extend the basic results on the theory of the generalized Riemann integral to the setting of bounded or locally nite measures on locally compact second countable Hausdorr spaces. The correspondence between Borel measures on X and continuous valuations on the upper space UX gives rise to a topological embedding between the space of locally nite measures and locally nite continuous valuations,...

By a hyperbolization of a locally compact non-complete metric space (X, d) we mean equipping X with a Gromov hyperbolic metric dh so that the boundary at infinity ∂∞X of (X, dh) can be identified with the metric boundary ∂X of (X, d) via a quasisymmetric map. The aim of this note is to show that the Gromov hyperbolic metric dh, recently introduced by the author, hyperbolizes the space X. In add...

It is shown that almost superdiagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces if the nonlocally convex linear topology τ(p i) is locally bounded. 1. Introduction. The purpose of this paper is to show that almost super-diagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces ...

in this short note, we have given a short proof for the existence of the haar measure on commutative locally compact hypergroups based on functional analysis methods by using markov-kakutani fixed point theorem.

This paper introduces a generalization of Pontryagin duality for locally compact Hausdorff abelian groups to locally compact Hausdorff abelian group bundles. First recall that a group bundle is just a groupoid where the range and source maps coincide. An abelian group bundle is a bundle where each fibre is an abelian group. When working with a group bundle G we will use X to denote the unit spa...