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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of a theorem by D. K. Faddeev
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by Konrad Behnen PDF
Proc. Amer. Math. Soc. 46 (1974), 51-58 Request permission

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.
References
  • Konrad Behnen, A characterization of certain rank-order tests with bounds for the asymptotic relative efficiency, Ann. Math. Statist. 43 (1972), 1839–1851. MR 373147, DOI 10.1214/aoms/1177690855
  • Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
  • Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
  • 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
  • I. P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Mathematische Lehrbücher und Monographien, Abteilung I: Mathematische Lehrbücher, Band VI, Akademie-Verlag, Berlin, 1969 (German). Übersetzung aus dem Russischen; Dritte Auflage; Herausgegeben von Karl Bögel. MR 0259033
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 46 (1974), 51-58
  • MSC: Primary 28A20; Secondary 62G05
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0352382-1
  • MathSciNet review: 0352382