重分形Hausdorff测度的有限测度子集(英文)

Subsets with Finite Measure of Multifractal Hausdorff Measures

英文关键词:multifractal Hausdorff measure  finite measure subset  net measure.

中文摘要:

      设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度，ｑ，ｔ∈Ｒ，记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度，证明了当μ为测度时，Ｈ_μ^q,t的有限测度子集存在．

英文摘要:

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