Multidimensional Riemann derivatives
Volume 235 / 2016
Studia Mathematica 235 (2016), 87-100
MSC: Primary 26B05, 26B35; Secondary 26A24, 26A27.
DOI: 10.4064/sm8578-7-2016
Published online: 3 October 2016
Abstract
The well-known concepts of $n$th Peano, Lipschitz, Riemann, Riemann Lipschitz, symmetric Riemann, and symmetric Riemann Lipschitz derivatives of real functions of a single variable have natural extensions to functions of several variables. We show that if a function has any of these $n$th derivatives at each point of a measurable subset of $\mathbb {R}^{d}$ then it has all these derivatives at almost every point of that subset.
