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

TL;DR

This paper investigates the properties of the Burkill-Cesari integral, demonstrating its symmetry and continuity, and introduces a new value concept on a subspace of absolutely continuous functions.

Contribution

It establishes the symmetry and continuity of the Burkill-Cesari integral and proposes a novel value on a specific subspace of absolutely continuous functions.

Findings

Proves the symmetry of the Burkill-Cesari integral.

Shows the integral's continuity in BV and Lipschitz norms.

Provides an existence result for a new value different from Aumann-Shapley's.

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 $AC_\infty$.