On the Decomposition of Distribution Function by Using Hausdorff Calculus

Abstract

This paper, by using Hausdorff calculus theory, decomposes farther a singular continuous distribution function into a sum of a series of absolute continuous distribution functions in different levels with respect to the Hausdorff measures and a singular continuous distribution function with respect to the Hausdorff measures. Consequently, it gives a more accurate decomposition formula for the distribution functions.