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Tibor Šalát; Vladimír Toma
A Classical Olivier’s Theorem and Statistical Convergence
Annales mathématiques Blaise Pascal, 10 no. 2 (2003), p. 305-313, doi: 10.5802/ambp.179
Article PDF | Reviews MR 2031274 | Zbl 1061.40001 | 2 citations in Cedram

Résumé - Abstract

L. Olivier proved in 1827 the classical result about the speed of convergence to zero of the terms of a convergent series with positive and decreasing terms. We prove that this result remains true if we omit the monotonicity of the terms of the series when the limit operation is replaced by the statistical limit, or some generalizations of this concept.

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