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2000
Issue 90

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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

90/2000

A Marstrand type theorem for measures with cube density in general dimension

Andrew Lorent

Abstract

With a view to generalising rectifiability and density results to more general spaces we prove the following: Let $H^{s}$ denote Hausdorff $s$ measure in $l_{\infty}^{n}$ . Let $s \in (0, 2]$ . Let $S \subset l_{\infty}^{n}$ be a subset of positive locally finite Hausdorff $s$ -measure with the property $lim_{r \to 0} \frac{H^{s} (B_{r} (x) \cap S)}{α (s) 2^{- s} r^{s}} = 1 for H^{s} a . e . x \in S$ then $s$ is an integer and $S$ has a weak tangent at almost every point-

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Received:: 09.01.01

Published:: 09.01.01

MSC Codes:: 28A75

Related publications

inJournal

2004 Repository Open Access

Andrew Lorent

A Marstrand type theorem for measures with cube density in general dimension

In: Mathematical proceedings of the Cambridge Philosophical Society, 137 (2004) 3, pp. 657-696

BibTex DOI: 10.1017/S0305004104007972