Critical values of set-valued maps with stratifiable graphs. Extensions of Sard and Smale-Sard theorems

摘要

We prove three theorems extending Sard's theorem and its infinite dimensional extension due to Smale to set-valued mappings with strati. able graphs. The very concept of a critical value comes from (nonsmooth) variational analysis and turns out to be perfectly compatible with the natural condition de. ning "good" strati. cations (e. g., Whitney strati. cation in the finite dimensional case).