  We compare two functionals defined on the space of continuous functions with
compact support in an open neighborhood of the zero section of the cotangent
bundle of a torus. One comes from Viterbo's symplectic homogenization while the
other from the Calabi quasi-states due to Entov and Polterovich. In dimension 2
we are able to say when these two functionals are equal. A partial result in
higher dimensions is presented. We also give a link to asymptotic Hofer
geometry on T^*S^1. Proofs are based on the theory of quasi-integrals and
topological measures on locally compact spaces.
