多重维测度的性质研究  

Study on Multi-measures

作　　者：顾国学[1] 喻祖国[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《工程数学学报》2012年第6期889-893,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071282);教育部新世纪人才计划项目(NCET-08-0686)~~

摘　　要：分形方法已被广泛应用于数学、物理、生物、工程甚至社会科学的研究中.江惠坤(1995)提出了Hausdorff测度和维数的推广形式—多重维测度和多重维数的概念.舒志彪(2002)利用多重维数和多重维测度对位势原理进行了推广,得到了分形集多重维数的下界估计,研究了它的一些性质.本文在他们工作的基础上继续探讨多重维数和多重测度的性质,还研究了多重网测度并证明了其与多重维测度的等价性.Fractal method has been widely used in the many fields such as mathematics, physics, biology, engineering, even social science. Hui-kun Jiang （1995） proposed the concepts of multi-measure and multi-dimension, which is an extension of the Hausdorff measure and dimension, respectively. Zhi- biao Shu （2002） used the generalized principle of potential about multi-measure and multi-dimension to deduce a lower bound of the multi-dimension of fractal sets and studied its properties. In this paper, we continue to study the properties of the multi-dimension of fractal sets. Furthermore, we also investigate the multiple net measure and prove that the multiple net measure is equivalent to the multi-measure.

关 键 词：HAUSDORFF测度与维数 多重维测度 多重维数 网测度与多重网测度 

分 类 号：O174.12[理学—数学]