相关论文: On a convergence of positive continuous additive f…
The relationship between smooth measures and positive continuous additive functionals is well known, and this correspondence is called the Revuz correspondence. We investigate the relationships between several types of convergence of smooth…
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
We provide necessary and sufficient conditions for the convergence of Revuz measures of finite energy integrals. More precisely, the Revuz map from the set of all smooth measures of finite energy integrals, equipped with the topology…
In this paper, we consider standard processes that admit dual processes and satisfy the absolute continuity condition, i.e., processes possess transition densities. For such processes, the Revuz correspondence relates positive continuous…
In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…
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…
The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on $\mathbb{R}^n$. The degree of compactness will be measured in terms of related entropy numbers. We are more…
Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient topological measures on locally compact spaces. Such an…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Let $X$ be a locally compact topological space, $(Y,d)$ be a boundedly compact metric space and $LB(X,Y)$ be the space of all locally bounded functions from $X$ to $Y$. We characterize compact sets in $LB(X,Y)$ equipped with the topology of…
In this article, we introduce the notions of sequentially compactness and boundedly compactness in the framework of a newly defined $b_v(s)$-metric space which is a generalization of usual metric spaces and several other abstract spaces. We…
A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and…
Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set…
In this article we introduce and study a natural form of expansivity, that we call \textit{metric-independent expansiveness}, for group actions on metrizable spaces. This notion means \textit{expansive with respect to every compatible…
If we consider a sequence of warped product length spaces, what conditions on the sequence of warping functions implies compactness of the sequence of distance functions? In particular, we want to know when a subsequence converges to a well…
We show that the space of continuous functions over a compact space X admits an equivalent pointwise-lowersemicontinuous locally uniformly rotund norm whenever X admits a fully closed map onto a compact Y such that C(Y) and the spaces of…
On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and…
We introduce a natural definition of $L^p$-convergence of maps, $p \ge 1$, in the case where the domain is a convergent sequence of measured metric space with respect to the measured Gromov-Hausdorff topology and the target is a…