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Convergence of best entropy estimates. (English) Zbl 0756.41037
Best estimation of quantities of interest is an important problem arising in several areas of sciences, engineering and technology. Here the authors consider the best entropy estimate, namely that nonnegative density with the given moments which minimizes the Boltzmann-Shannon entropy I. Strongly convex functions, $$L_ 1$$ convergence, error bounds and uniform convergence, classical algebraic and trigonometric moment problems are treated in detail. A direct proof is given to the effect that I has the Kadec property. The paper is a very valuable addition to the existing literature on the subject.

##### MSC:
 41A99 Approximations and expansions 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy 05C38 Paths and cycles
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