Related papers: On the weak-hash metric for boundedly finite integ…
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…
Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the…
We study the validity of a partition property known as weak indivisibility for the integer and the rational Urysohn metric spaces. We also compare weak indivisiblity to another partition property, called age-indivisibility, and provide an…
In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
Precise definitions of "weak [quantum] measurements" and "weak value" [of a quantum observable] are offered, which seem to capture the meaning of the often vague ways that these terms are used in the literature. Simple finite dimensional…
This article fits in the context of the approach to topological problems in terms of the underlying convergence space structures, and serves as yet another illustration of the power of the method. More specifically, we spell out…
We prove in this short report that for arbitrary weak converging sequence of sigma-finite Borelian measures in the separable Banach space there is a compact embedded separable subspace such that this measures not only are concentrated in…
We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague…
In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in…
We expand our effective framework for weak convergence of measures on the real line by showing that effective convergence in the Prokhorov metric is equivalent to effective weak convergence. In addition, we establish a framework for the…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…
A uniformly continuously integrable sequence of real-valued measurable functions, defined on some probability space, is relatively compact in the $\sigma(L^1,L^\infty)$ topology. In this paper, we link such a result to weak convergence…
We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact…
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…