The Burkill-Cesari integral as a semivalue on subspaces of AC

Abstract

We prove the simmetry of the Burkill-Cesari integral and discuss its continuity with respect to both the $BV$ norm of Aumann and Shapley and to the Lipschitz norm. As a consequence, we provide an existence result of a value, different from the Aumann and Shapley's one, on a subspace of $A{C}_{\infty }$.