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On (L1)* for General Measure Spaces

Published online by Cambridge University Press:  20 November 2018

H. W. Ellis  and
D. O. Snow
H. W. Ellis
Affiliation:
Queen's University, Summer Research Institute of the Canadian Mathematical Congress
D. O. Snow
Affiliation:
Queen's University, Summer Research Institute of the Canadian Mathematical Congress
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It is well known that certain results such as the Radon-Nikodym Theorem, which are valid in totally σ -finite measure spaces, do not extend to measure spaces in which μ is not totally σ -finite. (See §2 for notation.) Given an arbitrary measure space (X, S, μ) and a signed measure ν on (X, S), then if ν ≪ μ for X, ν ≪ μ when restricted to any e ∊ Sf and the classical finite Radon-Nikodym theorem produces a measurable function ge(x), vanishing outside e, with

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 2 , May 1963 , pp. 211 - 229
Copyright
Copyright © Canadian Mathematical Society 1963

References

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5. Schwartz, J. T., A note on the space Lp , Proc. Amer. P Math. Soc. 2, 1951, 270-75.Google Scholar