On statistical boundedness of metric valued sequences

Abstract

In this work, statistical boundedness is defined in ametric space and, statistical boundedness of metric valued sequences and their subsequences are studied. The interplay between the statistical boundedness and boundedness in a metric spaces are also studied, and it is shown that boundedness imply statistical boundedness and if the number of elements of the metric space is finite then these two concepts coincide. Moreover, here is given analogy of Balzano-Weierstrass Theorem.