THE POINTWISE DENSITIES OF NON-SYMMETRIC CANTOR SETS

We consider a class of non-symmetric Cantor sets C determined by C = a0C ∪ (a1C + 1 - a1), a0, a1 ∈ (0, 1). Under certain conditions on a0 and a1, the upper and lower densities are obtained explicitly for each x ∈ C. It extends the results for symmetric Cantor sets obtained by Feng, Hua and Wen (The pointwise densities of the Cantor measure, J. Math. Anal. Appl.250 (2000) 692–705).