Inserted: 24 jan 2005
Last Updated: 6 mar 2007
published in: European congress of mathematics, Stockholm, June 27--July 2, 2004. A. Laptev (ed.). European Mathematical Society, Zürich 2005.
We describe a decomposition result for Lebesgue negligible sets in the plane, and outline some applications to real analysis and geometric measure theory. Further results and detailed proofs are contained in a forthcoming paper by the same authors.
Keywords: functions of bounded variation, decomposition of null sets, Rademacher theorem, differentiability of Lipschitz maps, Dilworth's lemma