Convexity with given infinite weight sequences.
Zoltán Daróczy, Zsolt Páles (1987)
Stochastica
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Convexity with given infinite weight sequences.
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In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives...
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