Annales Academić Scientiarum Fennicć
Mathematica
Volumen 36, 2011, 677-681

RADIAL PROJECTIONS OF RECTIFIABLE SETS

Tuomas Orponen and Tuomas Sahlsten

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 Helsinki, Finland; tuomas.orponen 'at' helsinki.fi

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 Helsinki, Finland; tuomas.sahlsten 'at' helsinki.fi

Abstract. We show that if no m-plane contains almost all of an m-rectifiable set E \subset Rⁿ, then there exists a single (m - 1)-plane V such that the radial projection of E has positive m-dimensional measure from every point outside V.

2010 Mathematics Subject Classification: Primary 28A75; Secondary 28A78, 28A80.

Key words: Rectifiability, projections, Hausdorff measures.

Reference to this article: T. Orponen and T. Sahlsten: Radial projections of rectifiable sets. Ann. Acad. Sci. Fenn. Math. 36 (2011), 677-681.

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doi:10.5186/aasfm.2011.3634