A note on the parameterisation of Besicovitch sets.

Toby C O'Neil

Uploaded to arXiv:0901.3456v1 on 22nd January 2009.


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.

A postscript and pdf file of the preprint are available.

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Created:22 January 2009
Modified:29 January 2009