A Dichotomy Principle for Universal Series

V. Farmaki; V. Nestoridis

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008), p. 93-104 / Harvested from The Polish Digital Mathematics Library

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Résumé

Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence ${(α_{j})}_{j = 1}^{\infty}$ of scalars, there exists a subsequence ${(α_{k_{j}})}_{j = 1}^{\infty}$ such that either every subsequence of ${(α_{k_{j}})}_{j = 1}^{\infty}$ defines a universal series, or no subsequence of ${(α_{k_{j}})}_{j = 1}^{\infty}$ defines a universal series. In particular examples we decide which of the two cases holds.

Publié le : 2008-01-01

Zbl 1146.05048

EUDML-ID : urn:eudml:doc:281182

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V. Farmaki; V. Nestoridis. A Dichotomy Principle for Universal Series. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 93-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-1/