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- W2144996858 abstract "We consider the disintegration of the Lebesgue measure on the graph of a convex function f : R n → 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." @default.
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- W2144996858 date "2010-06-01" @default.
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- W2144996858 title "The disintegration of the Lebesgue measure on the faces of a convex function" @default.
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- W2144996858 doi "https://doi.org/10.1016/j.jfa.2010.01.024" @default.
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