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

Authors:	Richard Delaware

Affiliation:	Department of Mathematics and Statistics, Haag Hall Room 206, University of Missouri - Kansas City, 5100 Rockhill Rd., Kansas City, Missouri 64110

Abstract:	A set $Esubseteq mathbb{R} ^{n}$ is -straight if has finite Hausdorff -measure equal to its Hausdorff -content, where is continuous and non-decreasing with . Here, if satisfies the standard doubling condition, then every set of finite Hausdorff -measure in $mathbb{R} ^{n}$ is shown to be a countable union of -straight sets. This also settles a conjecture of Foran that when $h(t)=t^{s}$ , every set of finite -measure is a countable union of -straight sets.

Keywords:	$h$-straight Hausdorff measure Hausdorff content

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