The disintegration of the Lebesgue measure on the faces of a convex function (Q971825)

A convex function from \(\mathbb{R}^n\) to~\(\mathbb R\) has a natural decomposition: the decomposition into the interiors of its faces. The authors prove a disintegration theorem for Lebesgue measure restricted to the graph of such a function and show in particular that the measure on a \(k\)-dimensional face is equivalent to the \(k\)-dimensional Hausdorff dimension.