00974nas a2200109 4500008004300000245008100043210006900124520059700193100002100790700001700811856003600828 2010 en_Ud 00aThe disintegration of the Lebesgue measure on the faces of a convex function0 adisintegration of the Lebesgue measure on the faces of a convex 3 aWe 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.1 aCaravenna, Laura1 aDaneri, Sara uhttp://hdl.handle.net/1963/3622