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Concours général de 1874

Moret-Blanc (1875)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Differentiation of n-convex functions

H. Fejzić, R. E. Svetic, C. E. Weil (2010)

Fundamenta Mathematicae

The main result of this paper is that if f is n-convex on a measurable subset E of ℝ, then f is n-2 times differentiable, n-2 times Peano differentiable and the corresponding derivatives are equal, and f ( n - 1 ) = f ( n - 1 ) except on a countable set. Moreover f ( n - 1 ) is approximately differentiable with approximate derivative equal to the nth approximate Peano derivative of f almost everywhere.

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