The multifractal dimension functions of homogeneous Moran measure

摘要

In this paper we attain the multifractal dimension functions of Moran measure associated with homogeneous Moran fractals and give a sufficient condition which ensures the multifractal spectrum of Moran measure is equal to the Legendre transform of the multifractal dimension functions. As an application of this method, we give an example and a counterexample about the validity of the multifractal formalism of Moran measure.