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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Representation of vector valued nonlinear functions


Authors: Victor J. Mizel and K. Sundaresan
Journal: Trans. Amer. Math. Soc. 159 (1971), 111-127
MSC: Primary 47.80; Secondary 28.00
MathSciNet review: 0279647
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Abstract: A representation theorem for ``additive'' nonlinear functional on spaces $ {L^p}(\mu )$ is here extended to ``additive'' nonlinear functions from Lebesgue-Bochner function spaces $ L_E^p(\mu )$ ($ E$ a separable Banach space) into Banach spaces $ B$. A counterexample is provided to show that the restriction to separable $ E$ is essential.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0279647-8
Keywords: Additive functions, Carathéodory functions, locally uniformly continuous in variation, Lebesgue-Bochner function spaces, Bochner measurable
Article copyright: © Copyright 1971 American Mathematical Society