## The disintegration of the Lebesgue measure on the faces of a convex function (2009)

by
L. Caravenna
,
S. Daneri

Citations: | 3 - 1 self |

### BibTeX

@MISC{Caravenna09thedisintegration,

author = {L. Caravenna and S. Daneri},

title = {The disintegration of the Lebesgue measure on the faces of a convex function },

year = {2009}

}

### OpenURL

### Abstract

We consider the disintegration of the Lebesgue measure on the graph of a convex function f: R n → 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