@mastersthesis {2011,
	title = {Dimensional Reduction and Approximation of Measures and Weakly Differentiable Homeomorphisms},
	year = {2011},
	school = {SISSA},
	abstract = {This thesis is devoted to the study of two different problems: the properties of the disintegration of the Lebesgue measure on the faces of a convex function and the existence of smooth approximations of bi-Lipschitz orientation-preserving homeomorphisms in the plane.},
	url = {http://hdl.handle.net/1963/5348},
	author = {Sara Daneri}
}
@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 = {<p>We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-\&gt; \\\\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.</p>},
	doi = {10.1016/j.jfa.2010.01.024},
	url = {http://hdl.handle.net/1963/3622},
	author = {Laura Caravenna and Sara Daneri}
}
