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 ?? ?1 and 0 ?????+?,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 speed?(n)(?:N?R+is a monotonically increasing function with lim n???(n)=+?)andlim n??(?(n+1)-?(n)=0),have Hausdorff dimensionH(?)/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).