Open Access
1999/2000 On Series with Alternating Signs in the Euclidean Metric
Martin Dindoš
Real Anal. Exchange 25(2): 599-616 (1999/2000).


This paper presents one of many interesting aspects of relatively convergent series. Namely, given a sequence of elements of a Hilbert space we consider all possible ways of placing plus or minus signs in front of these elements to create an alternating sequence. In a convenient metric it makes sense to ask what is the `size' of the set of those choices of $+$ or $-$ for which the resulting series converges. The term `size' here refers to either Baire category or Lebesgue measure of this set. It turns out that especially the question of the Lebesgue measure of this set is quite intriguing and leads to interesting results generalizing known results for real-valued sequence.


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Martin Dindoš. "On Series with Alternating Signs in the Euclidean Metric." Real Anal. Exchange 25 (2) 599 - 616, 1999/2000.


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

zbMATH: 1011.40002
MathSciNet: MR1778513

Primary: 28A03 , 28A21 , 54E52
Secondary: 40A05

Keywords: $\ell^2$ theorem , Baire category , Euclidean metric , Lebesgue measure , relatively convergent series

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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