Rearrangement of conditionally convergent series on a small set

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:362

Article

Filipow, Rafal¹  Szuca, Piotr¹ 

[1] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland

关键词: Riemann's theorem;    Bolzano-Weierstrass property;    Positive Summability Property;    Statistical density;    Rearrangement of series;    Extending ideals;    Summable ideals;    Analytic ideals;    P-ideals;   

DOI  :  10.1016/j.jmaa.2009.07.029

来源: Elsevier

【 摘 要 】

We consider ideals I of subsets of the set of natural numbers such that for every conditionally convergent series Sigma(n is an element of omega) a(n) and every r is an element of (R) over bar there is a permutation pi(r) : omega -> omega such that Sigma(n is an element of omega) a(pi r(n)) = r and {n is an element of omega : pi(r)(n) not equal n} is an element of I. We characterize such ideals in terms of extendability to a summable ideal (this answers a question of Wilczynski). Additionally, we consider Sierpinski-like theorems. where one can rearrange only indices with positive a(n). (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free