Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1971-0280666-6
MathSciNet review: 0280666
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28.25

Retrieve articles in all journals with MSC: 28.25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0280666-6
Keywords: Variation, outer measure, upper integral, Lebesgue integral, Lebesgue space
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society