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A generalization of a theorem by D. K. Faddeev

Author: Konrad Behnen
Journal: Proc. Amer. Math. Soc. 46 (1974), 51-58
MSC: Primary 28A20; Secondary 62G05
MathSciNet review: 0352382
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Abstract: In this paper we give a simple proof of the statement $ {\lim _{n \to \infty }}\int {{K_n}(x,y)f(y)d\mu (y) = f(x)}$ for $ \mu $-almost all $ x$ under weaker and more general assumptions than those of the usual Faddeev theorems.

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  • [1] Konrad Behnen, A characterization of certain rank-order tests with bounds for the asymptotic relative efficiency, Ann. Math. Statist. 43 (1972), 1839–1851. MR 0373147,
  • [2] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [3] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325
  • [4] Jaroslav Hájek and Zbyněk Šidák, Theory of rank tests, Academic Press, New York-London; Academia Publishing House of the Czechoslovak Academy of Sciences, Prague, 1967. MR 0229351
  • [5] I. P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Übersetzung aus dem Russischen. Dritte Auflage. Herausgegeben von Karl Bögel. Mathematische Lehrbücher und Monographien. Abteilung I: Mathematische Lehrbücher, Band VI, Akademie-Verlag, Berlin, 1969 (German). MR 0259033

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Article copyright: © Copyright 1974 American Mathematical Society

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