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An Abstract Formulation of the Lebesgue Decomposition Theorem

Published online by Cambridge University Press:  09 April 2009

V. Ficker
V. Ficker
Affiliation:
Department of Mathematics University of NewcastleNew South Wales
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Some concepts in measure theory can be generalized by means of classes of null sets. When measures are considered then the classes of all sets of measure zero play the role of classes of null sets. The purpose of this paper is to give an abstract formulation and proof of the Lebesgue decomposition theorem.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1971 , pp. 101 - 105
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Ficker, V., ‘Dominated classes and related questions’, Acta Fac. Rerum Natur. Univ. Comenian 10, 7, (1966), 3–18.Google Scholar
[2]Ficker, V., ‘On the equivalence of a countable disjoint class of sets of positive measure and a weaker condition than total σ-finiteness of measures’, Bull. Austral. Math. Soc. 1 (1969), 237–243.CrossRefGoogle Scholar
[3]Halmos, P. R., Measure Theory (Van Nostrand, New York, 1950).CrossRefGoogle Scholar
[4]Johnson, R. A., ‘On the Lebesgue decomposition theorem’, Proc. Amer. Math. Soc. 18 (1967), 628–632.CrossRefGoogle Scholar