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Quasi-states and the Poisson bracket on surfaces

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  • We present a convexity-type result concerning simple quasi-states on closed manifolds. As a corollary, an inequality emerges which relates the Poisson bracket to 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.
    Mathematics Subject Classification: Primary: 53D99 Secondary: 28C15.

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