相关论文: Lower semicontinuity of monotone functionals in th…

We study Saks spaces of functions with values in a normed space and the associated mixed topologies. We are interested in properties of such Saks spaces and mixed topologies which are relevant for applications in the theory of bi-continuous…

In the dual $L_{\Phi^*}$ of a $\Delta_2$-Orlicz space $L_\Phi$, that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology…

In this work we derive a convex dual representation for increasing convex functionals on a space of real-valued Borel measurable functions defined on a countable product of metric spaces. Our main assumption is that the functionals fulfill…

For a given bi-continuous semigroup T on a Banach space X we define its adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak…

Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…

This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested…

This paper aims to study the dual of an extended locally convex space. In particular, we study the weak and weak* topologies as well as the topology of uniform convergence on bounded subsets of an extended locally convex space. As an…

We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…

In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…

This paper studies topological duals of Banach function spaces (BFS). We assume a finite measure but our arguments extend to general locally convex function spaces whose topology is generated by seminorms that satisfy the usual BFS axioms.…

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…

Let $X$ and $Y$ be topological spaces, let $Z$ be a metric space, and let $f: X\times Y\to Z$ be a mapping. It is shown that when $Y$ has a countable base $\mathcal B$, then under a rather general condition on the set-valued mappings $X\ni…

We study continuity and discontinuity of the upper and lower (modified) box-counting, Hausdorff, packing, (modified) correlation measure-dimension mappings under the weak, setwise and TV topology on the space of Borel measures respectively…

We consider the convexity properties of distortion functionals, particularly the linear distortion, defined for homeomorphisms of domains in Euclidean $n$-spaces, $n\geq 3$. The inner and outer distortion functionals are lower…

A function $F$ defined on all subsets of a finite ground set $E$ is quasi-concave if $F(X\cup Y)\geq\min\{F(X),F(Y)\}$ for all $X,Y\subset E$. Quasi-concave functions arise in many fields of mathematics and computer science such as social…

Multimarginal optimal transport (MOT) has gained increasing attention in recent years, notably due to its relevance in machine learning and statistics, where one seeks to jointly compare and align multiple probability distributions. This…

We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…

When $X$ is locally compact, a quasi-integral (also called a quasi-linear functional) on $ C_c(X)$ is a homogeneous, positive functional that is only assumed to be linear on singly-generated subalgebras. We study simple and almost simple…