Remark 3.39 . [02LK]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Remark 3.39.

When some of the $f_{i}$ , say $f_{1},\dots,f_{k}$ , are piecewise affine, the statement (3) of the previous proposition holds under the weaker hypothesis [Roc70, Theorem 20.1]

{\operatorname{dom}}(f_{1})\cap\dots\cap{\operatorname{dom}}(f_{k})\cap\operatorname{ri}({\operatorname{dom}}(f_{k+1}))\cap\dots\cap\operatorname{ri}({\operatorname{dom}}(f_{l}))\not=\emptyset.