2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125094We present a convexity-type result concerning simple quasi-states on closed manifolds. As a corollary, an inequality emerges which relates the Poisson bracket and the measure of non-additivity of a simple quasi-state on a closed surface equipped with an area form. In addition, we prove that the uniform norm of the Poisson bracket of two functions on a surface is stable from below under C^0-perturbations.14 pagesSymplectic GeometryFunctional Analysis53D99; 28C15text