Every set of finite Hausdorff measure is a countable union of sets whose Hausdorff measure and content coincide

DOI10.1090/S0002-9939-02-06825-9zbMath1012.28005MaRDI QIDQ4804109

Richard Delaware

Publication date: 10 April 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Hausdorff measureHausdorff content\(h\)-straight

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Hausdorff and packing measures (28A78)

Related Items (8)

On the equality of Hausdorff measure and Hausdorff content ⋮ Some results on the upper convex densities for the self-similar sets ⋮ A decomposition for Borel measures \(\mu \le \mathcal{H}^s \) ⋮ Elementary density bounds for self-similar sets and application ⋮ Graphs of convex functions are \(\sigma\)1-straight ⋮ Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure ⋮ Furstenberg sets for a fractal set of directions ⋮ Connecting Hausdorff measure and upper convex density or \(H^s\)-a.e. covering

Cites Work

• Sets whose Hausdorff measure equals method I outer measure.
• Measure preserving continuous straightenings of fractional-dimensional sets
• Graphs of convex functions are \(\sigma\)1-straight
• Graphs of functions, regular sets and \(s\)-straight sets
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