Construction of measures and integrals
HTML articles powered by AMS MathViewer
- by B. S. Thomson PDF
- Trans. Amer. Math. Soc. 160 (1971), 287-296 Request permission
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
- 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
- Ralph Henstock, Theory of integration, Butterworths, London, 1963. MR 0158047 —, Linear analysis, Butterworths, London, 1967.
- Ralph Henstock, Generalized integrals of vector-valued functions, Proc. London Math. Soc. (3) 19 (1969), 509–536. MR 251189, DOI 10.1112/plms/s3-19.3.509
- E. J. McShane, A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals, Memoirs of the American Mathematical Society, No. 88, American Mathematical Society, Providence, R.I., 1969. MR 0265527
Additional Information
- © Copyright 1971 American Mathematical Society
- 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