The relative multifractal analysis, review and examples

In the present paper, we suggest new proofs of many known results about the relative multifractal formalism. We provide results even at points q for which the relative multifractal Hausdorff and packing functions differ. We also give some examples of two measures where the multifractal functions are different and the Hausdorff dimension of the level sets of the v-local Holder exponent is given by the Legendre transform of the multifractal Hausdorff function and their packing dimension by the Legendre transform of the multifractal packing function.