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Zbl 0883.40003
Fridy, J.A.; Orhan, C.
Statistical limit superior and limit inferior.
(English)
[J] Proc. Am. Math. Soc. 125, No. 12, 3625-3631 (1997). ISSN 0002-9939; ISSN 1088-6826/e

Summary: Following the concept of statistical convergence and statistical cluster points of a sequence $x$, we give a definition of statistical limit superior and inferior which yields natural relationships among these ideas: e.g., $x$ is statistically convergent if and only if st-$\liminf x=\text{st-}\limsup x$. The statistical core of $x$ is also introduced, for which an analogue of Knopp's core theorem is proved. Also, it is proved that a bounded sequence that is $C_1$-summable to its statistical limit superior is statistically convergent.
MSC 2000:
*40C05 Matrix methods in summability
26A03 Elementary topology of the real line
40A05 Convergence of series and sequences

Keywords: Natural density; statistically convergent sequence; statistical cluster point; core of a sequence

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