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The Projection of a Linear Functional on the Manifold of Integrals

Published online by Cambridge University Press:  20 November 2018

H. Gordon  and
E. R. Lorch
H. Gordon
Affiliation:
Barnard College Columbia University New York
E. R. Lorch
Affiliation:
Barnard College Columbia University New York
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If μ is a measure defined on a space and fn(x) is a sequence of μ-integrable functions converging to f(x), then under suitable conditions of boundedness, one has the theorem of Lebesgue that

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Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 465 - 474
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Lorch, E. R., Abstract 250t, Bull. Amer. Math. Soc, 60 (1954), 155.Google Scholar
2. Woodbury, M. A., Abstract 167t, Bull. Amer. Math. Soc, 56 (1950), 171.Google Scholar
3. Yosida, K. and Hewitt, E., Finitely additive measures, Trans. Amer. Math. Soc, 72(1952), 46–66.Google Scholar