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On extremal points of the unit ball in the Banach space of Lipschitz continuous functions

Part of: General convexity Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

S. Rolewicz
S. Rolewicz
Affiliation:
Instytut Matematuczny, Polskiej Akademii Nauk, Sniadeckich 8, 00 950 Warszawa, Poland
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Abstract

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It is shown that for arbitrary ε > 0 there is a function x(t, x) defined on the square [0,1] × [0,1] such that x(t, s) represents an extremal point of the unit ball in the space of Lipschitz continuous functions, and the gradient of x(t, s) is equal to 0 except on a set of measure at most ε.

Keywords

convexityChoquet theoryconvex sets in topological vector spaces

MSC classification

Secondary: 46A55: Convex sets in topological linear spaces; Choquet theory 52A07: Convex sets in topological vector spaces

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 1 , August 1986 , pp. 95 - 98
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Rolewicz, S., ‘On optimal observability of Lipschitz systems’, in Selected topics in operations research and mathematical economics, Lecture Notes in Economics and Mathematical Systems 226, Springer-Verlag, pp. 151–158.Google Scholar