@article {2010,
title = {The disintegration of the Lebesgue measure on the faces of a convex function},
journal = {J. Funct. Anal. 258 (2010) 3604-3661},
number = {SISSA;24/2009/M},
year = {2010},
abstract = {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.},
doi = {10.1016/j.jfa.2010.01.024},
url = {http://hdl.handle.net/1963/3622},
author = {Laura Caravenna and Sara Daneri}
}