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Journal of Convex Analysis 21 (2014), No. 2, 449--452
Copyright Heldermann Verlag 2014

Differentiability of the "Positive Part" Map

Michel Valadier
Dép. des Mathématiques, Université Montpellier II, Place Eugène Bataillon, Case Courier 051, 34095 Montpellier Cedex, France

This is a 1964 work which was quoted in some papers (in 1966, 1976) but remained unpublished. We hope the results and the hypotheses of the statements will still find some echo. We give here the English translation of the article "Un problème de dérivabilité dans Lp'', Séminaire d'Automatique Théorique, Université de Caen (France), November 27 (1964), only avoiding an archaical presentation of Uniform Integrability and suppressing two examples.

Keywords: L-p-spaces, positive part of a function, Frechet differentiability, Gateaux differentiability.

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