Convergence of best phi -entropy estimates

Minimization problems involving phi -entropy functionals (a generalization of Boltzmann-Shannon entropy) are studied over a given set A and a sequence of sets A/sub n/ and the properties of their optimal solutions x/sub phi /, x/sub n/. Under certain conditions on the objective functional and the sets A and A/sub n/, it is proven that as n increases to infinity, the optimal solution x/sub n/ converges in L/sub 1/ norm to the test phi -entropy estimate x/sub phi /.<
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