一类广义Cantor集的Hausdorff测度

Hausdorff Measure of Generalized Cantor Sets

研究和推广了自相似分形中最经典的例子Cantor三分集的构造及其Hausdorff测度 ,解决了一类广义Cantor集的Hausdorff测度计算问题 .得到的主要结果是构造了一类广义的Cantor 2k + 1(k∈N)分集 ,并证明了它们的Hausdorff测度Hs(E) =1.

A generalized Cantor set which is a classical case in self similar fractal is constructed and its Hausdorff measure is discussed. The construction of the generalized Contor 2k+1(k∈N) fractal sets and their measures H s(E)=1 are also presented.