We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

%B J. Funct. Anal. 258 (2010) 3604-3661 %G en_US %U http://hdl.handle.net/1963/3622 %1 682 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-24T15:53:31Z\\nNo. of bitstreams: 1\\ndisconvCaravDaneri.pdf: 759110 bytes, checksum: e22e069339fc07c3bde1855b76e61d1e (MD5) %R 10.1016/j.jfa.2010.01.024