Abstract
Let ν be a probability measure on Ω . We define the upper and lower multifractal box dimension (the measure ν with respect to μ ) on a probability space and investigate the relation between the multifractal box dimension and the multifractal Hausdorff dimension, the multifractal pre-packing dimension . Then, we generalize the dimension inequalities of multifractal Hausdorff measures and multifractal packing measures in a probability space.
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