Measures and Two Point Set
نویسندگان
چکیده
We investigate the question: under which conditions is a-compact partial two point contained in a two point set? We show that no reasonable measure or capacity (when applied to the set itself) can provide a suucient condition for a compact partial two point set to be extendable to a two point set. On the other hand, we prove that under Martin's Axiom any-compact partial two point set such that its square has Hausdorr 1-measure zero is extendable.
منابع مشابه
SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS
In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...
متن کاملCommon Zero Points of Two Finite Families of Maximal Monotone Operators via Proximal Point Algorithms
In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...
متن کاملON TRUNCATED MEASURES OF INCOME INEQUALITY FROM A FUZZY PERSPECTIVE
In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating t...
متن کاملBest proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
متن کاملUniquely classifying flexible measures by a CWS model
Data Envelopment Analysis (DEA) deals with evaluating a set of decision-making units (DMUs) based on nonparametric mathematical approaches. In classical DEA models, the given set of factors of DMUs is divided into two categories, inputs and outputs, while in some practical problems there are some measures whose membership to these categories is unclear. It means these factors treat different in...
متن کاملSome local fixed point results under $C$-class functions with applications to coupled elliptic systems
The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...
متن کامل