Related papers: Vague and basic convergence of signed measures

We formulate a simple characterization of homogeneous Young measures associated with measurable functions. It is based on the notion of the quasi-Young measure introduced in the previous article published in this Journal. First, homogeneous…

The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured…

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…

One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued functions is defined. Using this integral,…

In this paper, we will study the continuity of the Fourier transform of measures with respect to the vague topology. We show that the Fourier transform is vaguely discontinuous on R, but becomes continuous when restricting to a class of…

The Frechet mean or barycenter generalizes the idea of averaging in spaces where pairwise addition is not well-defined. In general metric spaces, the Frechet sample mean is not a consistent estimator of the theoretical Frechet mean. For…

An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note,…

This note describes Fatou's lemma and Lebesgue's dominated convergence theorem for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to…

We prove uniform convergence of metrics $g_k$ on a closed surface with bounded integral curvature (measure) in the sense of A.D. Alexandrov, under the assumption that the curvature measures $\mathbb{K}_{g_k}=\mu^1_k-\mu^2_k$, where…

We propose a convergence mode for positive Radon measures which allows a sequence of probability measures to have an improper limiting measure. We define a sequence of vague priors as a sequence of probability measures that converges to an…

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…

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.

We extend almost everywhere convergence in Wiener-Wintner ergodic theorem for $\sigma$-finite measure to a generally stronger almost uniform convergence and present a larger, universal, space for which this convergence holds. We then extend…

We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a…

We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…

We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the…

We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set of homomorphisms in the form of a measure…

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

In 1987, I. Labuda proved a general representation theorem that, as a special case, shows that the topology of local convergence in measure is the minimal topology on Orlicz spaces and $L_{\infty}$. Minimal topologies connect with the…

We investigate three aspects of weak* convergence of the $n$-step distributions of random walks on finite volume homogeneous spaces $G/\Gamma$ of semisimple real Lie groups. First, we look into the obvious obstruction to the upgrade from…