DECIMAL SET WITH ZERO MEASURE AND FULL HAUSDORFF DIMENSION

摘要

LetFλ ={x∈ (0,1){2nx} ≥1/2k,n∈ z+}, z++ = {0,1,2,3,...}, k∈ N;F = U∞k=1Fλ be a decimal set in (0, 1), where {2nx} is the fractional part of a number 2nx. In this note, we prove that dirnнF = 1 and Н1(F) = 0, where dimн is Hausdr off dimension, and Н1(F) is the Hausdorff measure of F.