一类广义Cantor集的Hausdorff测度

Analysis on Hausdorff Measurement of a Kind of Extended Cantor Sets

讨论了线性迭代系统si(x)=aix+ci,i=1,2,3在满足开集条件时,产生的广义Cantor集E与F,并获得了E与F的s维Hausdorff测度的精确值,即Hs(E)=1,Hs(F)=c31-a3-c11-a1s,其中s满足as1+as2+as3=1。

Extended Cantor Sets E and F is produced when a linear iterated satisfying the open sets condition Furthemore , a computational formula of the system si（x）=aix＋ci,i=1,2,3 on the Hausdorff measure of extended Cantor sets E and F given,H^s（E）=1,Hs（F）=[c3/1-a3-c1/1-a1]^s which satisfy a1^s＋a2^s＋a3^s=1.