Set valued integrability in non separable Fr'{e}chet spaces and applications

We focus on measurability and integrability for set valued functions in non-necessarily separable Fr'{e}chet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide useful characterizations of Pettis set-valued integrability in the announced framework. Finally, we indicate applications to Volterra integral inclusions.