Related papers: Partial orders on metric measure spaces
In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders. In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed…
We study the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. The post-processing order is fundamental as it enables to compare measurements by their intrinsic noise and it…
In the paper we are dealing with metric measure spaces of diameter at most one and of total measure one. Gromov introduced the sampling compactification of the set of these spaces. He asked whether the metric measure space invariants extend…
In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
As shown by A. Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial…
Partial orders are used extensively for modeling and analyzing concurrent computations. In this paper, we define two properties of partially ordered sets: width-extensibility and interleaving-consistency, and show that a partial order can…
We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their…
A metric measure space is a complete separable metric space equipped with probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on…
The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders…
This paper concerns the development of partial and semi-partial measures of spatial associations in the context of multivariate spatial lattice data which describe global or local associations among spatially aggregated measurements for…
Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with…
Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…
We provide a formal definition and study the basic properties of partially ordered chains (POC). These systems were proposed to model textures in image processing and to represent independence relations between random variables in…
In this paper we combine the notions of partial metric spaces with negative distances, $G_p$-metric spaces and n-metric spaces together into one structure called the partial n-metric spaces. These are generalizations of all the said…
In this paper we are going to prove a very general fixed point theorem for mappings acting in partial metric spaces. In that theorem we impose some conditions on behavior of considered mappings on orbits and a condition relating orbits of…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
In this book, we study Gromov's metric geometric theory on the space of metric measure spaces, based on the idea of concentration of measure phenomenon due to L\'evy and Milman. Although most of the details are omitted in the original…
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures.…