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Weak Compactness and Vector Measures

Published online by Cambridge University Press:  20 November 2018

R. G. Bartle ,
N. Dunford  and
J. Schwartz
R. G. Bartle
Affiliation:
Yale University
N. Dunford
Affiliation:
Yale University
J. Schwartz
Affiliation:
Yale University
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Introduction. It is the purpose of this paper to develop a Lebesgue theory of integration of scalar functions with respect to a countably additive measure whose values lie in a Banach space. The class of integrable functions reduces to the ordinary space of Lebesgue integrable functions if the measure is scalar valued. Convergence theorems of the Vitali and Lebesgue type are valid in the general situation. The desirability of such a theory is indicated by recent developments in spectral theory.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 289 - 305
Copyright
Copyright © Canadian Mathematical Society 1955

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