连续函数微切集的存在性定理

数学物理学报

连续函数微切集的存在性定理

赵培标; 杨孝平

(南京理工大学应用数学系南京 210094; 南京理工大学理学院南京 210094)

收稿日期:2005-12-01 修回日期:2007-06-22 出版日期:2008-10-25 发布日期:2008-10-25
通讯作者: 赵培标
基金资助:
国家自然科学基金(10771102)、教育部博士点基金(2003028802)、江苏省自然科学基金 (BK2006209)及南京理工大学科研发展基金(AB96137)资助

Existence Theorem of Micro-Tangent Sets of Continuous Functions

Zhao Peibiao; Yang Xiaoping

(Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094)

Received:2005-12-01 Revised:2007-06-22 Online:2008-10-25 Published:2008-10-25
Contact: Zhao Peibiao

摘要/Abstract

摘要： 该文研究了在Hausdorff 度量及分布意义下连续函数之微切集的存在性问题, 证明了连续的典型函数具有丰富的(万有)微切集结构. 这一结果推广了Z. Buczolich^[3]的相关结论.

关键词: 微切集, 典型连续函数, 切测度, Rectifiable集, 剩余集

Abstract: We prove the existence theorem: there are many Micro-tangent sets of each function of some residual set of c [0,1] in the sense of Hausdorff metric and that of distribution, respectively. In other words, the typical continuous function has a rich (universal) micro-tangent set structure at many points. This generalizes the results offered by Z.Buczolich [1].

Key words: Micro-tangent set, Typical continuous function, Tangent measures, Rectifiable set, Residual set

中图分类号:

26C20

赵培标; 杨孝平. 连续函数微切集的存在性定理[J]. 数学物理学报, 2008, 28(5): 831-839.

Zhao Peibiao; Yang Xiaoping. Existence Theorem of Micro-Tangent Sets of Continuous Functions[J]. Acta mathematica scientia,Series A, 2008, 28(5): 831-839.