A NOTE ON OLIVIER'S THEOREM AND CONVERGENCE IN ERDOS-ULAM DENSITY
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Open Access
- 1 January 2020
- journal article
- research article
- Published by SCIK Publishing Corporation in International Journal of Analysis and Applications
- Vol. 18 (3) , 332-336
Abstract
Olivier's Theorem says that if Sigma a(n) is a convergent positive series and (a(n)) is monotone decreasing, then na(n) -> 0. Salat and Toma [4] proved that the monotonicity condition can be omitted if the convergence of (na(n))(n) is replaced by the statistical convergence. The aim of this note is to give an alternative proof and generalization of this result.Keywords
This publication has 2 references indexed in Scilit:
- Sets with countably infinitely many prescribed weighted densitiesRocky Mountain Journal of Mathematics, 2020
- A Classical Olivier’s Theorem and Statistical ConvergenceAnnales mathématiques Blaise Pascal, 2003