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Transactions of the American Mathematical Society

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



Construction of measures and integrals

Author: B. S. Thomson
Journal: Trans. Amer. Math. Soc. 160 (1971), 287-296
MSC: Primary 28.25
MathSciNet review: 0280666
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Abstract: The systems introduced by R. Henstock and later by E. J. McShane to provide powerful generalizations of the Riemann integral are used to construct outer measures and upper integrals and to develop a Lebesgue type theory in quite general settings.

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

  • [1] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [2] R. Henstock, Theory of integration, Butterworths, London, 1963. MR 28 #1274. MR 0158047 (28:1274)
  • [3] -, Linear analysis, Butterworths, London, 1967.
  • [4] -, Generalized integrals of vector-valued functions, Proc. London Math. Soc. (3) 19 (1969), 509-536. MR 40 #4420. MR 0251189 (40:4420)
  • [5] E. J. McShane, A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals, Mem. Amer. Math. Soc. No. 88 (1969). MR 0265527 (42:436)

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Keywords: Variation, outer measure, upper integral, Lebesgue integral, Lebesgue space
Article copyright: © Copyright 1971 American Mathematical Society

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