Advanced Search

In this paper we study the set of statistical cluster points of sequences in $m$-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in $m$-dimensional spaces too. We also define a notion of $\Gamma$-statistical convergence. A sequence $x$ is $\Gamma$-statistically convergent to a set $C$ if $C$ is a minimal closed set such that for every $ϵ>0$ the set $\{k\rho (C,x_k)\ge ϵ\}$ has density zero. It is shown that every statistically bounded sequence...