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.

引用

页码：943 / 956

页数：14

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