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# Article

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Keywords:
Banach space; Lipschitz surface; d.c. surface; multiplicity points of monotone operators; singular points of convex functions; Aronszajn null sets
Summary:
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated $\sigma$-ideals are studied. These $\sigma$-ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.
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