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In this chapter, we present the well-established theory of differentiability of first and second order for convex functions and their extensions to locally semiconvex functions. This will culminate in the essential theorem of Alexandrov on second order differentiability in the Peano sense on sets of full Lebesgue measure.

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Differentiability of Convex Functions

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  • 发表日期：

    2025年

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  • Kevin R. Payne,
  • Davide Francesco Redaelli

摘要

In this chapter, we present the well-established theory of differentiability of first and second order for convex functions and their extensions to locally semiconvex functions. This will culminate in the essential theorem of Alexandrov on second order differentiability in the Peano sense on sets of full Lebesgue measure.