| let S(x)={S1(x),S2(x)}.Where S1(x)=(?)x,S2(x)=(?)x+1/3.let F be the attractorof the IFS S(x)={S1(x),S2(x)},and we often call the invariant measureμis Cantor measure. Let S=log2/log3,we will determine by an explicit formula for every point x∈F, the upper and lower s-densitiesθ*s(μ,x),θ*s(μ,x) of the Cantor measure at the point x.In term of the 3-adic expansion of x .We show that there exists a countable setE(?)F,such that 9(2θ*s(μ,x))1/s+(2θ*s(μ,x))1/s=8 holds for F\E.Furthermore ,forμ-almost all x,θ*s(μ,x)=2-s,θ*s(μ,x)=2-s-1. |
