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The disintegration of the Lebesgue measure on the faces of a convex function

Abstract:

We consider the disintegration of the Lebesgue measure on the graph of a convex function f : Rn → 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 t...

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Publisher copy:
10.1016/j.jfa.2010.01.024

Authors


Caravenna, L More by this author
Journal:
Journal of Functional Analysis
Volume:
258
Issue:
11
Pages:
3604-3661
Publication date:
2010-06-01
DOI:
EISSN:
1096-0783
ISSN:
0022-1236
URN:
uuid:8d6c0704-d84c-468c-b060-1667141928b6
Source identifiers:
298422
Local pid:
pubs:298422

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