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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On everywhere-defined integrals


Author: Lester E. Dubins
Journal: Trans. Amer. Math. Soc. 232 (1977), 187-194
MSC: Primary 28A30
DOI: https://doi.org/10.1090/S0002-9947-1977-0450489-9
MathSciNet review: 0450489
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Abstract | References | Similar Articles | Additional Information

Abstract: Hardly any finite integrals can be defined for all real-valued functions. In contrast, if infinity is admitted as a possible value for the integral, then every finite integral can be extended to all real-valued functions.


References [Enhancements On Off] (What's this?)

  • [1] Bruno de Finetti, Theory of probability, Vol. 1, Wiley, New York, 1975
  • [2] Leonard J. Savage, The foundations of statistics, 2nd rev. ed., Dover, New York, 1972. MR 16, 147; 50 #1364. MR 0348870 (50:1364)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0450489-9
Keywords: Integration, measure, finite additivity, linear forms
Article copyright: © Copyright 1977 American Mathematical Society

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