相对重分形的维数  

THE DIMENSION RELATIVE MULTIFRACTAL

作　　者：陈磊[1] 戴朝寿[1] 

机构地区：[1]徐州师范大学数学系,徐州221116

出　　处：《南京大学学报（数学半年刊）》2005年第2期221-233,共13页Journal of Nanjing University(Mathematical Biquarterly)

摘　　要：本文将Julian Cole引入的一个概率测度关于另一概率测度的重分形形式体系里测度定义中的中心覆盖改为覆盖,得到与之等价的相对重分形测度和相同的维数,用两种不同方式定义了上、下盒维数,研究了各种维数的性质及相互关系,证明了相对重分形的Hausdorff维数函数和Packing维数函数是下凸的,讨论了它们在Legendre变换下的关系.Julian Cole introduced a general formalism for the multifractal analysisof one probability measure with respect to another and studied relative multifractalanalysis. In this paper, equivalent definitions of relative multifractal measure are intro-duced, the relative multifractal box dimensions in two different ways are defined, andthat they are equivalent under some conditions is proved. Moreover, we prove that therelative multifractal Hausdorff dimension and box dimension satisfy the usual relationand that the relative multifractal dimension function are convex. Finally, the relationbetween them under Legendre transformation is researched.

关 键 词：相对重分形 HAUSDORFF维数 PACKING维数 盒维数 Besicovitch覆盖定理 

分 类 号：O189.1[理学—数学]