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Generic differentiability of locally Lipschitz functions on product spaces. (English) Zbl 0847.58005

It is known that there is a minimality condition on the subdifferential mapping of the function which guarantees that the set of points of differentiability is a residual set. The author characterizes such minimality by a quasicontinuity property of the Dini derivatives of the function and derives sufficiency conditions for the generic differentiability of locally Lipschitz functions on a product space. The basic results are formulated in five theorems.

MSC:

58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
46G05 Derivatives of functions in infinite-dimensional spaces
46B20 Geometry and structure of normed linear spaces
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