Annales AcademiŠ Scientiarum FennicŠ
Mathematica
Volumen 32, 2007, 545-548

SETS OF FINITE H1 MEASURE THAT INTERSECT POSITIVELY MANY LINES IN INFINITELY MANY POINTS

Marianna Cs÷rnyei and David Preiss

University College London, Department of Mathematics
Gower Street, London WC1E 6BT, UK; mari 'at' math.ucl.ac.uk

University of Warwick, Mathematics Institute
Coventry, CV4 7AL, UK; D.Preiss 'at' warwick.ac.uk

Abstract. We construct a planar Borel set A of finite H1-measure such that through positively many points of A, positively many lines meet A at infinitely many points. This answers a question of Mattila.

2000 Mathematics Subject Classification: Primary 28A75.

Key words: Besicovitch's projection theorem, rectifiability, duality.

Reference to this article: M. Cs÷rnyei and D. Preiss: Sets of finite H1 measure that intersect positively many lines in infinitely many points Ann. Acad. Sci. Fenn. Math. 32 (2007), 545-548.

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