Monzner, AlexandraZapolsky, Frol2011-02-112011-02-112011-02-11http://hdl.handle.net/2003/2761610.17877/DE290R-15855We 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, 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.en610preprint