Abstract
It is shown that the set of points for which a monotone mappingT:X→X * from a separable Banach space into its dual is not single-valued has no interior; if dimX<∞ and intD(T)≠ϕ then the set has Lebesgue measure zero. Moreover, for accretive mappingsT:X→X from a separable Banach space into itself, the dimension of the set of points whose images contain balls of codimension not larger thank does not exceedk. Applications to convexity are given.
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Zarantonello, E.H. Dense single-valuedness of monotone operators. Israel J. Math. 15, 158–166 (1973). https://doi.org/10.1007/BF02764602
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DOI: https://doi.org/10.1007/BF02764602