Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-08T10:24:50.767Z Has data issue: false hasContentIssue false

On Integration of Vector-Valued Functions

Published online by Cambridge University Press:  20 November 2018

D. O. Snow*
Affiliation:
Acadia University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Among the variety of integrals which have been devised for integrating vector-valued functions the most widely used is that of Bochner (2), perhaps because of the simplicity of its formulation. Other approaches, including one by Birkhoff (1), have yielded more general integrals yet none of them seems to have supplanted the Bochner integral to a significant extent.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Birkhoff, Garrett, Integration of functions with values in a Banach space, Trans. Amer. Math. Soc, 88 (1935), 357-378.Google Scholar
2. Bochner, S., Integration von Funktionen deren Werte die Elemente eines Vektorraumes sind, Fund. Math., 20 (1933), 262-276.Google Scholar
3. Bourbaki, N., Intégration, Actualités Sci. Ind. 1175 (Paris, 1952).Google Scholar
4. Graves, L. M., Riemann integration and Taylor's theorem in general analysis, Trans. Amer. Math. Soc, 29 (1927), 163-177.Google Scholar
5. Hahn, H., Ueber eine Verallgemeinerung der Riemannschen Integral definition, Monatsh. Math. Phys., 26 (1915), 3-18.Google Scholar
6. Hildebrandt, T. H., Integration in abstract spaces, Bull. Amer. Math. Soc, 59 (1953), 111-139.Google Scholar
7. Jeffery, R. L., Integration in abstract space, Duke Math. J., 6 (1940), 706-718.Google Scholar
8.Macphail, M. S., Integration of functions in a Banach space, National Math. Magazine, 20 (1945), 69-78.Google Scholar
9. Saks, S., Theory of the Integral (Warsaw, 1937).Google Scholar