Multidimensional Riemann derivatives
Studia Mathematica, Tome 235 (2016) no. 1, pp. 87-100
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
well known concepts nth peano lipschitz riemann riemann lipschitz symmetric riemann symmetric riemann lipschitz derivatives real functions single variable have natural extensions functions several variables function has these nth derivatives each point measurable subset mathbb has these derivatives almost every point subset
Affiliations des auteurs :
J. Marshall Ash 1 ; Stefan Catoiu 2
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author = {J. Marshall Ash and Stefan Catoiu},
title = {Multidimensional {Riemann} derivatives},
journal = {Studia Mathematica},
pages = {87--100},
publisher = {mathdoc},
volume = {235},
number = {1},
year = {2016},
doi = {10.4064/sm8578-7-2016},
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TY - JOUR AU - J. Marshall Ash AU - Stefan Catoiu TI - Multidimensional Riemann derivatives JO - Studia Mathematica PY - 2016 SP - 87 EP - 100 VL - 235 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm8578-7-2016/ DO - 10.4064/sm8578-7-2016 LA - en ID - 10_4064_sm8578_7_2016 ER -
J. Marshall Ash; Stefan Catoiu. Multidimensional Riemann derivatives. Studia Mathematica, Tome 235 (2016) no. 1, pp. 87-100. doi: 10.4064/sm8578-7-2016
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