We derive two upper bounds for the probability of deviation a vector-valued Lipschitz function collection random variables from its expected value. The resulting can be tighter than obtained by direct application classical theorem due to Bobkov and Götze.

Relying on the notion of set-valued Lie bracket introduced in an earlier paper, we extend some classical results valid for smooth vector fields to the case when the vector fields are just Lipschitz. In particular, we prove that the flows of two Lipschitz vector fields commute for small times if and only if their Lie bracket vanishes everywhere (i.e., equivalently, if their classical Lie bracket...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.