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Complex extreme measurable selections

Part of: Classical measure theory Linear function spaces and their duals

Published online by Cambridge University Press:  09 April 2009

Douglas Mupasiri
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Abstract

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We give a characterization of complex extreme measurable selections for a suitable set-valued map. We use this result to obtain necessary and sufficient conditions for a function to be a complex extreme point of the closed unit ball of Lp (ω, Σ, ν X), where (ω, σ, ν) is any positive, complete measure space, X is a separable complex Banach space, and 0 < p < ∞.

MSC classification

Secondary: 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets 46E40: Spaces of vector- and operator-valued functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 2 , April 1995 , pp. 222 - 231
Copyright
Copyright © Australian Mathematical Society 1995

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