Abstract
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 Γ-statistical convergence. A sequence xis Γ-statistically convergent to a set Cif Cis a minimal closed set such that for every ∈ > 0 the set $$\{ k:\varrho (C,x_{{\text{ }}k} ) \geqslant \varepsilon \} $$ has density zero. It is shown that every statistically bounded sequence is Γ-statistically convergent. Moreover if a sequence is Γ-statistically convergent then the limit set is a set of statistical cluster points.
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