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SOME COMMENTS ON SCALAR DIFFERENTIATION OF VECTOR-VALUED FUNCTIONS

Part of: Real functions Normed linear spaces and Banach spaces; Banach lattices Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  11 November 2014

K. M. NARALENKOV
K. M. NARALENKOV*
Affiliation:
Moscow State Institute of International Relations, Department of Mathematical Methods and Information Technologies, Vernadskogo Ave. 76, 119454 Moscow, Russian Federation email naralenkov@gmail.com
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Abstract

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We make some comments on the existence, uniqueness and integrability of the scalar derivatives and approximate scalar derivatives of vector-valued functions. We are particularly interested in the connection between scalar differentiation and the weak Radon–Nikodým property.

Keywords

scalar and approximate scalar derivativessVB and sVBG functionsRadon–Nikodým and weak Radon–Nikodým propertiesLipschitz functionindefinite Riemann integral

MSC classification

Primary: 46G05: Derivatives
Secondary: 26A45: Functions of bounded variation, generalizations 46B22: Radon-Nikodým, Kreĭn-Milman and related properties 46G10: Vector-valued measures and integration
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 311 - 321
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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