华侨大学学报（自然科学版）Issue(6)：726-730,5.DOI:10.11830/ISSN.1000-5013.2015.06.0726
A-收敛与几乎处处收敛
On A-Convergence and Almost Usual Convergence
摘要
Abstract
Let A≡(ai )∞i=1 S +1 ,a sequence (xn )of points in a Banach X is said to be A-convergent to x ∈X provided that for anyε>0,lim i→∞〈ai ,χA(ε)〉=0,where A(ε)={n∈N∶‖xn -x‖≥ε}.In this paper,we give two different approa-ches of A-convergence via ideal on N and via extreme measures.We show that for any A≡(ai )∞i=1 S +1 ,there exist an i-deal IA and a collection P ext (IA )of extreme probability measures such that the A-convergence,the ideal IA-convergence and the measure P ext (IA )-convergence are equivalent.We also show that A-convergence equivalent to P ext (IA )-almost usu-al convergence if and only if it is nondegenerate.关键词
统计收敛/理想收敛/几乎处处收敛/极端测度/Banach 空间Key words
statistical convergence/ideal convergence/almost usual convergence/extreme measures/Banach space分类
数理科学引用本文复制引用
鲍玲鑫,施慧华..A-收敛与几乎处处收敛[J].华侨大学学报（自然科学版）,2015,(6):726-730,5.基金项目
国家自然科学基金专项数学天元基金资助项目（11426064，11426061）；国家自然科学基金青年基金资助项目（11401227，11501108）；福建省自然科学基金资助项目 （）
