R￣d中Hausdorff维数和packing维数的确定

THE DETERMINATION OF HAUSDORFF DIMENSION AND PACKING DIMENSION IN R￣d

本文目的在于建立确定Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ和ｐａｃｋｉｎｇ维数Ｄｉｍ的两个命题（定理１和定理２），进而寻求Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ与ｐａｃｋｉｎｇ维数Ｄｉｍ相等的条件；这使得我们能够引入分形测度的测度论定义。

The obiect of this note is to establish two propositions on de-termining the Hausdorff dimension dim and the packing dimension Dim inR￣d(Theorem 1 and Theorem 2),and further seek the conditions that the Hausdorffdimension dim is equal to the pachng dimension Dim in R￣d(Theorem 3);thusthis enable introduction of a measure theory definition of fractal measures.