The Hausdorff Centred measure of the symmetry Cantor sets

Let 0<λ≤1/3, K(λ) be the attractor of an iterated function system {ϕ₁ϕ₂} on the line, where ϕ₁(x)=λx, ϕ₁(x)=1-λ+λx,x∈[0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the 0123 0132 V 3 exact Hausdorff Centred measure of K(λ). This work is supported partially by the Foundation of the National Education Ministry, National Natural Scienctific Committee, Guangdong Province and Zhongshan University Advanced Research Center.