实轴上集序列的强渐近行为  

The Strong Asymptotic Behavior of Set Sequence on the Real Line

作　　者：李汉巨[1,2] 

机构地区：[1]华南师范大学,广州510631 [2]广东电网有限责任公司东莞供电局,东莞523008

出　　处：《应用泛函分析学报》2016年第4期383-391,共9页Acta Analysis Functionalis Applicata

摘　　要：首先基于点序列渐进分布的概念(分布函数是连续函数),提出实轴上集序列强渐近分布的概念(分布函数是绝对连续函数),是模1一致分布概念的推广.其次给出强渐近分布的Weyl型准则,改进Nakajima和Ohkubo的结果.最后利用强渐近分布的Weyl型准则研究一类实轴上迭代函数系统轨迹的强渐近行为.Firstly, based on the concept of asymptotic distribution of point sequence （the distribution function is a continuous function）, the concept of the strong asymp- totic distribution of set sequence on the real line （the distribution function is an ab- solutely continuous function） is proposed, which is a generalization of the concept of uniform distribution modulo one. Secondly, we give a Weyl＇s type criterion for strong asymptotic distribution, improving results of Nakajima and Ohkubo. Finally, we study the strong asymptotic behavior of orbits of certain iterated function systems on the real line, using the Weyl＇s type criterion of strong asymptotic distribution.

关 键 词：一致分布 渐近分布 强渐近分布 Weyl准则 迭代函数系统 

分 类 号：O156.4[理学—数学] O174.1[理学—基础数学]