The disintegration of the Lebesgue measure on the faces of a convex function
type: Item
instance of: scholarly article
title: The disintegration of the Lebesgue measure on the faces of a convex function
zbMATH Open document ID: 1202.28003
published in: Journal of Functional Analysis
publication date: 2010-05-17T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 28A50
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 5708620
zbMATH Keywords: convex function
zbMATH Keywords: disintegration of measures
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: Hausdorff measure
author: Laura Caravenna
author: Sara Daneri
reviewed by: K. P. Hart
MaRDI profile type: Publication
full work available at URL: j.jfa.2010.01.024
OpenAlex ID: W2144996858
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DOI: 10.1016/J.JFA.2010.01.024
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description: scientific article; zbMATH DE number 5708620