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1999/2000 On a Typical Series with Alternating Signs
Martin Dindoš
Real Anal. Exchange 25(2): 617-628 (1999/2000).


This paper presents a study of typical series with alternating signs. Namely, given a sequence of real nonnegative numbers whose sum is infinity we consider all possible ways of placing plus or minus signs in front of each of these numbers. Choosing a convenient metric we ask what is the `size' (in terms of Baire category and porosity) of the set of those choices of $+$ or $-$ for which the resulting series converges. The author of this paper has studied this problem in his paper [D1] for the Euclidean metric. The main goal of this paper is to extend the results from [D1] for other standard metrics, such as the Fr\`echet or Baire metrics.


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Martin Dindoš. "On a Typical Series with Alternating Signs." Real Anal. Exchange 25 (2) 617 - 628, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 3 January 2009

zbMATH: 1011.40003
MathSciNet: MR1778514

Primary: 28A21 , 40A05 , 54E52
Secondary: 28A05

Keywords: Baire category , Fr\`echet and Baire metric , porosity , relatively convergent series

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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