Real analysis: inequalities, the continuum property, induction, sequences, functions and limits, continuity, contraction mappings and fixed points, differentiation, mean value theorems and Taylor's ...

We present here three results concerning holomorphic functions on inductive limits of $C^{N}$ (N finite or countably infinite). The first result is a positive one ...

Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.

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