Related papers: Induced Measures on "Mu**"- measurable Sets
We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such…
We deal with finitely additive measures defined on all subsets of natural numbers which extend the asymptotic density (density measures). We consider a class of density measures which are constructed from free ultrafilters on natural…
For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
Based on the ideas of {\it quantum extension} and {\it quantum conditioning}, we propose a generic approach to construct a new kind of entanglement measures called {\it conditional entanglement}. The new measures, built from the known…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli…
We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module of derivations into free modules; [2] the existence of a…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Psychosocial constructs can only be assessed indirectly, and measures are typically formed by a combination of indicators that are thought to relate to the construct. Reflective and formative measurement models offer different…
We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme…
We define a notion of coordinatization for $\aleph_0$-categorical structures which is, like Lie coordinatized structures in [2], a certain kind of expansion of a tree. We show that a structure which is coordinatized, in a certain strong…
We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The…