an:01506734
Zbl 0963.28004
Huang, Lihu; Yu, Jinghu
Subsets with finite measure of multifractal Hausdorff measures
EN
J. Math. Res. Expo. 20, No. 2, 166-170 (2000).
00065055
2000
j
28A78
measure; Borel probability measure; multifractal Hausdorff measure; Federer condition; finite-measure subsets
Summary: Let \(\mu\) be a Borel probability measure on \(\mathbb{R}^d\), \(q,t\in\mathbb{R}\). Let \({\mathcal H}^{q,t}_\mu\) denote the multifractal Hausdorff measure. We prove that, when \(\mu\) satisfies the so-called Federer condition for a closed subset \(E\in\mathbb{R}^n\) such that \({\mathcal H}^{q,t}_\mu(E)> 0\), there exists a compact subset \(F\) of \(E\) with \(0<{\mathcal H}^{q,t}_\mu(F)< \infty\), i.e., finite-measure subsets of multifractal Hausdorff measure exist.