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$%M. Yahdi, The topological complexity of sets of convex differentiable functions, Rev. Mat. Complut. 11 (1998), no. 1, 79–91. %$

Let be the set of all convex and continuous functions on a separable infinite dimensional Banach space , equipped with the topology of uniform convergence on bounded subsets of . We show that the subset of all convex Fréchet-differentiable functions on , and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on , reduce every coanalytic set, in particular they are not Borel-sets.

1991 Mathematics Subject Classification: 54H05, 46B20, 58C20.