Related papers: Weak Minkowski Spaces
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
We prove a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type. We also apply this result to study isoperimetric problems with repulsive interaction terms, under convexity constraints. We show…
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…
We introduce a framework for Riemannian diffeology. To this end, we use the tangent functor in the sense of Blohmann and one of the options of a metric on a diffeological space in the sense of Iglesias-Zemmour. As a consequence, the…
The Marcinkiewicz integral is essentially a Littlewood-Paley $g$-function, which plays a important role in harmonic analysis. In this article, by using the atomic decomposition theory of weighted Hardy spaces and homogeneous weighted…
We study the metric structure of walks on graphs, understood as Lipschitz sequences. To this end, a weighted metric is introduced to handle sequences, enabling the definition of distances between walks based on stepwise vertex distances and…
We analyze weak convergence on CAT(0) spaces and the existence and properties of corresponding weak topologies.
In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of…
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 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…
We introduce the metric space valued in partially ordered groups, and define the convergence of sequences and the multi-valued weak contractions, etc., on the space. We then establish endpoint theorems for the defined maps. Our…
A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…
In this paper, we study the Randers metrics of weakly isotropic scalar curvature. We prove that a Randers metric of weakly isotropic scalar curvature must be of isotropic $S$-curvature. Further, we prove that a conformally flat Randers…
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz. We assume either an appropriate measure growth condition with respect to the effective resistance…
We give a short review of a construction of Frink to obtain a metric space from a quasi-metric space. By an example we illustrate the limits of the construction.
We prove two weak compactness criteria in Musielak-Orlicz spaces for $N$-functions satisfying the $\Delta_2$-condition. They extend criteria from And\^o for Orlicz spaces to this setting of non-symmetrical Banach function spaces. As…
Weak-type quasi-norms are defined using the mean oscillation or the mean of a function on dyadic cubes, providing discrete analogues and variants of the corresponding quasi-norms on the upper half-space previously considered in the…
To appear in J. Funct. Spaces and Appl.
In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…
The space of Minkowski valuations on an m-dimensional complex vector space which are continuous, translation invariant and contravariant under the complex special linear group is explicitly described. Each valuation with these properties is…