THE POINTWISE DENSITIES OF NON-SYMMETRIC CANTOR SETS

摘要

We consider a class of non-symmetric Cantor sets C determined by C = a(0)C boolean OR (a(1)C + 1 - a(1)), a(0), a(1) epsilon (0, 1). Under certain conditions on a(0) and a(1), the upper and lower densities are obtained explicitly for each x epsilon 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).