Dense Single-Valuedness of Monotone Operators.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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It is shown that the set of points where a monotone mapping T X maps to X from a separable Banach space into its dual is not single valued has no interior if dim X infinity and int Dt not equal phi then the set has Lebesgue measure zero. Moreover, for accretive mappings T X maps to X form a separable Banach space into itself the dimensions of the set of points whose images contain balls of codimension not larger than k does not exceed k. Applications to convexity are given. Author
- Theoretical Mathematics