Related papers: Vague and basic convergence of signed measures
It is well known that besides oscillations, sequences bounded only in $L^1$ can also develop concentrations, and if the latter occurs, we can at most hope for weak$^*$ convergence in the sense of measures. Here we derive a new tool to…
Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures…
In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's…
We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…
We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $S=\Gamma\backslash G/K$ is compact. More precisely, given a sequence of homogeneous probability…
We show weak convergence of quantile and expectile processes to Gaussian limit processes in the space of bounded functions endowed with an appropriate semimetric which is based on the concepts of epi- and hypo convergence as introduced in…
A signed polygonal measure is the sum of finitely many real constant density measures supported on polygons. Given a finite set S in the plane, we study the existence of signed polygonal measures spanned by polygons with vertices in S,…
We prove that an approximated version of the Brunn--Minkowski inequality with volume distortion coefficient implies a Gaussian concentration-of-measure phenomenon. Our main theorem is applicable to discrete spaces.
The aim of this paper is to introduce several notions of homogenization in various classes of weighted means, which include quasiarithmetic and semideviation means. In general, the homogenization is an operator which attaches a homogeneous…
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…
We provide a unified framework to proving pointwise convergence of sparse sequences, deterministic and random, at the $L^1(X)$ endpoint. Specifically, suppose that \[ a_n \in \{ \lfloor n^c \rfloor, \min\{ k : \sum_{j \leq k} X_j = n\} \}…
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan \cite{FanETDS}, and to dilated series, including Davenport…
Let $G = (V,E)$ be a connected graph. A probability measure $\mu$ on $V$ is called "balanced" if it has the following property: if $T_\mu(v)$ denotes the "earth mover's" cost of transporting all the mass of $\mu$ from all over the graph to…
In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with…
The topic of this paper is the typical behavior of the spectral measures of large random matrices drawn from several ensembles of interest, including in particular matrices drawn from Haar measure on the classical Lie groups, random…
Let X be an infinite compact metric space with finite covering dimension. Let $\afhpa,\bt: X\to X$ be two minimal homeomorphisms. Suppose that the range of $K_0$-groups of both crossed product C*-algebras s are dense in the space of real…
Given a finite Borel measure $\mu$ on R n and basic semi-algebraic sets $\Omega$\_i $\subset$ R n , i = 1,. .. , p, we provide a systematic numerical scheme to approximate as closely as desired $\mu$(\cup\_i $\Omega$\_i), when all moments…
We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypothesis for (families of) Markov chains on finite configuration space in some asymptotic regime, including the case of configuration space size…
We study the limiting object of a sequence of Markov chains analogous to the limits of graphs, hypergraphs, and other objects which have been studied. Following a suggestion of Aldous, we assign to a sequence of finite Markov chains with…