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Topological measure spaces: two counter-examples

Published online by Cambridge University Press:  24 October 2008

D. H. Fremlin
D. H. Fremlin
Affiliation:
University of Essex
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Extract

The ‘Radon measures’ of N. Bourbaki(1) enjoy many striking properties. Among the most important of these is the ‘strong Radon-Nikodým theorem’ that the dual of L1-(μ) can always be identified with L∞(μ) ((1), chap. 5, §5, no. 8, theorem 4). As this is certainly not true of non-σ-finite measures in general, it is natural to ask what are the special properties on which it relies.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 1 , July 1975 , pp. 95 - 106
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Bourbaki, N.Éléments de mathématique, vol. VI (Intégration). (Hermann, 1965, 1967, 1969.)Google Scholar
(2)Fremlin, D. H.Topological Riesz spaces and measure theory (Cambridge University Press, due 1974).CrossRefGoogle Scholar
(3)Hewitt, E. and Stromberg, K.Real and abstract analysis (Springer, 1969).Google Scholar
(4)Tulcea, A. Ionescu and , C.Topics in the theory of lifting (Springer, 1969).CrossRefGoogle Scholar
(5)Halmos, P. R.Measure Theory (van Nostrand, 1950).CrossRefGoogle Scholar