107 research outputs found
Non-existence of multi-line Besicovitch sets
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.Comment: 7 pages. v2: corrected typos and added references, to appear in Publ.
Ma
Tangent measures of non-doubling measures
We construct a non-doubling measure on the real line, all tangent measures of
which are equivalent to Lebesgue measure.Comment: 17 pages, 5 figures. v2: Minor corrections throughout, and section
six completely rewritten in a more reader-friendly style; Accepted to Math.
Proc. Cambridge Philos. So
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