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arXiv · 0901.3456

A note on the parameterisation of Besicovitch sets

Toby C. O'Neil
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Abstract

In response to a question raised (and answered in the negative) by Terry Tao on his blog as to whether it is possible to rotate a line segment continuously within a set of area zero, we show that there is a set of area zero in the plane within which a line segment can be rotated by a Baire-1 map.

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Toby C. O'Neil. 2009-01-22. A note on the parameterisation of Besicovitch sets. https://arxiv.org/abs/0901.3456

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