Author(s)

Muquan Yan

Department of Mathematics, South China University of Technology, Guangzhou, China.

The main purpose of this note is to estimate the size of the set T_μλ of points, at which the Cantor function is not differentiable and we find that the Hausdorff dimension of T_μλ is [log2/log3]². Moreover, the Packing dimension of T_μλ is log2/log3. The log2 = log_e2 is that if a^x = N (a >0, and a≠1), then the number x is called the logarithm of N with a base, recorded as x = log_aN, read as the logarithm of N with a base, where a is called logarithm Base number, N is called true number.

Hausdor Dimension, Packing Dimension, Cantor Ternary Function, Cantor Ternary Set

Yan, M. (2020) Dimension of the Non-Differentiability Subset of the Cantor Function. Journal of Applied Mathematics and Physics, 8, 107-114. doi: 10.4236/jamp.2020.81009.