Density versions of Schur's theorem for ideals generated by submeasures

被引：10
|
作者：
Filipow, Rafal [1 ]
Szuca, Piotr [1 ]
机构：
[1] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2010年 / 117卷 / 07期
关键词：
Bolzano-Weierstrass theorem; Bolzano-Weierstrass property; Ideal convergence; Statistical density; Statistical convergence; Subsequence; Schur's theorem;
D O I：
10.1016/j.jcta.2009.12.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterize ideals of subsets of natural numbers for which some versions of Schur's theorem hold. These are similar to generalizations shown by Bergelson (1986) in [1] and Frankl, Graham and Rodl (1990) in [7]. Additionally, we prove a generalization of an iterated version of Ramsey's theorem. (C) 2009 Elsevier Inc. All rights reserved.
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页码：943 / 956
页数：14
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