Geodesic
Statistical cluster points of sequences in finite dimensional spaces
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 95-102.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $\epsilon > 0 $ the set $ \lbrace k\:\rho (C, x_k ) \ge \epsilon \rbrace $ has density zero. It is shown that every statistically bounded sequence is $\Gamma $-statistically convergent. Moreover if a sequence is $\Gamma $-statistically convergent then the limit set is a set of statistical cluster points.
Classification : 11B05, 40A05
Keywords: compact sets; natural density; statistically bounded sequence; statistical cluster point 
@article{CMJ_2004__54_1_a7,
     author = {Pehlivan, S. and G\"uncan, A. and Mamedov, M. A.},
     title = {Statistical cluster points of sequences in finite dimensional spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {95--102},
     publisher = {mathdoc},
     volume = {54},
     number = {1},
     year = {2004},
     mrnumber = {2040222},
     zbl = {1045.40004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a7/}
}
TY  - JOUR
AU  - Pehlivan, S.
AU  - Güncan, A.
AU  - Mamedov, M. A.
TI  - Statistical cluster points of sequences in finite dimensional spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 95
EP  - 102
VL  - 54
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a7/
LA  - en
ID  - CMJ_2004__54_1_a7
ER  - 
%0 Journal Article
%A Pehlivan, S.
%A Güncan, A.
%A Mamedov, M. A.
%T Statistical cluster points of sequences in finite dimensional spaces
%J Czechoslovak Mathematical Journal
%D 2004
%P 95-102
%V 54
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a7/
%G en
%F CMJ_2004__54_1_a7
Pehlivan, S.; Güncan, A.; Mamedov, M. A. Statistical cluster points of sequences in finite dimensional spaces. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 95-102. http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a7/