The Hessian measures of a (semi-)convex function can be introduced as coefficients of a local Steiner formula. The investigation of Hessian measures is continued by the provision of a geometric characterization of the support of these measures. Then the Radon–Nikodym derivative and the absolute continuity of Hessian measures with respect to Lebesgue measure are explored. As special cases of the results, known results for surface area measures of convex bodies are recovered.

Hessian measures of convex functions and applications to area measures / A. COLESANTI; D. HUG. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 71 (2):(2005), pp. 221-235.

Hessian measures of convex functions and applications to area measures

COLESANTI, ANDREA;
2005

Abstract

The Hessian measures of a (semi-)convex function can be introduced as coefficients of a local Steiner formula. The investigation of Hessian measures is continued by the provision of a geometric characterization of the support of these measures. Then the Radon–Nikodym derivative and the absolute continuity of Hessian measures with respect to Lebesgue measure are explored. As special cases of the results, known results for surface area measures of convex bodies are recovered.
2005
71 (2)
221
235
A. COLESANTI; D. HUG
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/251065
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