2020
DOI: 10.48550/arxiv.2005.03269
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Pointwise densities of homogeneous Cantor measure and critical values

Derong Kong,
Wenxia Li,
Yuanyuan Yao

Abstract: Let N ≥ 2 and ρ ∈ (0, 1/N 2 ]. The homogenous Cantor set E is the self-similar set generated by the iterated function systemLet s = dimH E be the Hausdorff dimension of E, and let µ = H s |E be the s-dimensional Hausdorff measure restricted to E. In this paper we describe, for each x ∈ E, the pointwise lower s-density Θ s * (µ, x) and upper s-density Θ * s (µ, x) of µ at x. This extends some early results of Feng et al. (2000). Furthermore, we determine two critical values ac and bc for the sets E * (a) = {x ∈… Show more

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