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On the Pringsheim Rearrangement Theorems

โœ Scribed by Marion Scheepers

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
140 KB
Volume
267
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

We show that requiring that the set of positions of the positive terms in a conditionally convergent numerical series have asymptotic density provides converses for old rearrangement theorems of Alfred Pringsheim.

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## Abstract Let us call a finite subset __X__ of a Euclidean __m__โ€space E^m^ __Ramsey__ if for any positive integer __r__ there is an integer __n__ = __n__(__X;r__) such that in any partition of E^n^ into __r__ classes __C__~1~,โ€ฆ, __C~r~__, some __C~i~__ contains a set __X__' which is the image of