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Let (f(n)) be a sequence of functions converging in norm to f in some rotund Orlicz function or se-quence space endowed with the Luxemburg norm or the Orlicz norm, and let (C(n)) be a sequence of convex sets satisfying some condition and tending in suitable way to a ser C. Then the best norm approximation of f(n) with respect to C(n) converges in norm to the best approximation of f with respect to...
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