Non-existence of multi-line Besicovitch sets

Tuomas Orponen

Type: Article

Publication Date: 2013-12-18

Citations: 0

DOI: https://doi.org/10.5565/publmat_58114_10

Abstract

If a compact set K \subset R^2 contains a positive-dimensional family of line-segments in positively many directions, then K has positive measure.

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Works Cited by This (5)

Action	Title	Year	Authors
+ PDF Chat	An X-ray transform estimate in $\mathbb R^n$	2001	Izabella Łaba Terence Tao
+	Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability	1995	Pertti Mattila
+	Besicovitch type maximal operators and applications to fourier analysis	1991	Jean Bourgain
+	The Kakeya Maximal Function and the Spherical Summation Multipliers	1977	Antonio Cordóba
+	The geometry of fractal sets	1985	K. J. Falconer