The disintegration of the Lebesgue measure on the faces of a convex function
Caravenna L, Daneri S (2010)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2010
Journal
Publisher: Elsevier
Book Volume: 258
Pages Range: 3604-3661
Journal Issue: 11
DOI: 10.1016/j.jfa.2010.01.024
Abstract
We consider the disintegration of the Lebesgue measure on the graph of a convex function f : R → 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 on 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. © 2010 Elsevier Inc. All rights reserved.
Authors with CRIS profile
Involved external institutions
Italy (IT)How to cite
APA:
Caravenna, L., & Daneri, S. (2010). The disintegration of the Lebesgue measure on the faces of a convex function. Journal of Functional Analysis, 258(11), 3604-3661. https://dx.doi.org/10.1016/j.jfa.2010.01.024
MLA:
Caravenna, Laura, and Sara Daneri. "The disintegration of the Lebesgue measure on the faces of a convex function." Journal of Functional Analysis 258.11 (2010): 3604-3661.
BibTeX: Download