Multifractal dimension inequalities in a probability space (Q2468068)

Let \(\nu \) be a probability measure on \(\varOmega \). The authors define the upper and lower multifractal box dimension (the measure \(\nu \) with respect to \(\mu \)) on a probability space and investigate the relation between the multifractal box dimension and the multifractal Hausdorff dimension, the multifractal pre-packing dimension. Then, they generalize the dimension inequalities of multifractal Hausdorff measures and multifractal packing measures in a probability space.