A quantitative version of the Besicovitch projection theorem via multiscale analysis

Details A quantitative version of the Besicovitch projection theorem via multiscale analysis A quantitative version of the Besicovitch projection theorem via multiscale analysis

2007-06-18

arxiv.org/abs/0706.2646v2

Mathematics

Classical Analysis and ODEs

30 pages, 6 figures. Submitted, J. Lond. Math. Soc. Some revisions based on initial referee report

Scientific paper

By using a multiscale analysis, we establish quantitative versions of the Besicovitch projection theorem (almost every projection of a purely unrectifiable set in the plane of finite length has measure zero) and a standard companion result, namely that any planar set with at least two projections of measure zero is purely unrectifiable. We illustrate these results by providing an explicit (but weak) upper bound on the average projection of the $n^{th}$ generation of a product Cantor set.

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