Titlebook: General Inequalities 1 / Allgemeine Ungleichungen 1; Proceedings of the F E. F. Beckenbach Conference proceedings 1978 Springer Basel AG 19

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Inequalities and Functional Equations in the Theory of the Price IndexFive axioms which play a role in the theory of the price index are introduced in the form of inequalities and functional equations. It is shown that there exists a subset of four of these axioms which are independent and which imply the fifth one.

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On Lipschitz Condition and Zygmund’s Property for Functions of Several VariablesThe literature contains results on the relation between the smoothness of a real function f of several real variables and the degree of approximation to f by splines. The purpose of the present note is to study two elementary cases and to derive the corresponding results by simple methods, allowing the range of f to lie in a general space.

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Inequalities Related to the Normal LawIn the important case of a symmetric distribution, it is shown that the familiar approximation leading to the normal law is actually an estimate from above. A more elementary inequality is presented first; this is much easier to prove than the final result, but it leads, nevertheless, to the solution of a nontrivial maximizing problem.

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Bound on the Measure of a Set in a Product SpaceA simple bound is obtained for the measures of certain sets in product spaces. The bound is a kind of Chernoff bound.

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