| Let ( be a Borel Probability measure on Rd. q, t,∈ R. Let Hμq,t denote the multifractal Hausdorff measure. We prove that, when satisfies the so-called Federer condition, for a closed subset E∈Rn, such that Hμq,t(E) > 0, there exists a compact subset F of E with 0 < Hμq,t(F) <∞ , i.e, the finite measure subsets of multifractal Hausdorff measure exist. |
