A quantitative version of the Besicovitch projection theorem via multiscale analysis

Abstract

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 nth generation of a product Cantor set.

Locations

• Proceedings of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• arXiv (Cornell University) - PDF
• DataCite API - View
• Proceedings of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• arXiv (Cornell University) - PDF
• DataCite API - View