Hausdorff测度H^s(F)与H_δ~s(F)的关系

The relationship between Hausdorff measure H^s(F) and H_δ~s(F)

在对满足开集条件的自相似分形的测度关系进行了分析的基础上,对一般分形的Hausdorff测度的对应关系进行了讨论.给出了Rn中任意集合F,当s>dimH(F)时,Hs(F)与Hsδ(F)相等的结论;对Rn中任意有界集合F,当s<dimH(F)时,获得了Hsδ(F)<Hs(F)的证明.对于一般分形的相应测度关系给出了一个系统的推测.

On the basis of analysis of the measure relations of the self-similar fractal meeting open set condition by literature before,this paper discusses corresponding relations of the Hausdorff measure of general fractal.For any set F in Rn,Hs（F）Hδs（F） when sdimH（F）;For any Bounded set F,there is always Hs（F）Hδs（F） when sdimH（F）.A speculate of the measuring relationship of general fractals has been given.