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A generalisation of the radon-nikodym theorem

Published online by Cambridge University Press:  09 April 2009

P. D. Finch
P. D. Finch
Affiliation:
Monash University
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Let be a space of points x, a σ-field of subsets of a σ-finite measure on . The elements of will be called measurable sets and all the sets considered in this paper are measurable sets. A real-valued point function t(x) on will be said to be measurabl if, for each real α, the set {x: t(x)≦ α} is measurable. Let (S), S C denote the σ-field of all measurable subsets of S. A real-valued function f(·) on will be called a set function.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 1 , February 1965 , pp. 17 - 24
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Finch, P. D., Integration of real-valued set functions in abstract spaces, This Journal 4 (1964), 202–213.Google Scholar
[2]Finch, P. D., The theory of information and statistical inference I, Journ. App. Prob. I (1964), 121–140.CrossRefGoogle Scholar
[3]Royden, H. L., Real Analysis. Macmillan, New York (1963).Google Scholar