Weak Local Dimension on Deranged Cantor Sets

Abstract

We define weak local dimension at each point in a deranged Cantor set. Using this, we classify the deranged Cantor set into a multifractal structure which is useful for computing the Hausdorff dimension and the packing dimension of the deranged Cantor set. Finally, we give examples in which the weak local dimensions are used for the calculation of the dimensions in a deterministic case and a probabilistic case.