Sections and extensions of concave functions
Necessary and sufficient conditions are given that a collection \(\phi_ i\), \(1\leq i\leq \ell\), of continuous, non-negative, concave functions on \({\mathbb{R}}^{n+}\) can all be realized as parallel sections of a single continuous, non-negative, concave function \(\psi\) on \({\mathbb{R}}^{m+}\), for some \(m\geq n\). This result shows at least the mathematical possibility of defining fundamental preferences in the sense of \textit{S.- Ch. Kolm} [''Justice et equité'', CNRS, Paris (1972)]. An analogous result for quasi-convex functions is also proved.
scientific article; zbMATH DE number 4005947
scientific article