Hausdorff Dimension Of The Intersections Of The Besicovitch Sets And The Exceptional Erd(?)s-Rényi Sets

Researchers are interested in the relationship between the Besicovitch sets and Erd(?)s-Rényi sets in recent years.There are some results have been proposed,but there is still a lot of promotion work needs to be done in this field.In this paper,we prove that,for any 0 ≤α ≤1 and 0 ≤β≤γ≤+∞,the sets (?) which are the intersections of the Besicovitch sets and the relevant exceptional Erd(?)s-Renyi sets in which the Rn(x)of the point has the general asymptotic behavior with respect to the more general speedψ(n)(ψ:N→R+is a monotonically increasing function with lim n→∞ψ(n）=+∞)andlim n→∞(ψ(n+1）-ψ(n）=0),have Hausdorff dimensionH(α)/log2,where Sn(x)denotes the summation of the first n digits of x and Rn(x)is the maximal length of 1’s in the first n digits of the dyadic expansion of x ∈[0,1).