A sufficient condition for the differentiation of certain classes of set functions
Published online by Cambridge University Press: 24 October 2008
Extract
We shall be concerned with the differentiation of an arbitrary set function ψ from certain classes of set functions with respect to another fixed set function φ. In (1), § 2·5, a halo evanescence condition is shown to be necessary and sufficient for the differentiation of a fixed measure ψ with respect to φ. Here we formulate a type of halo condition which ensures the differentiability of entire classes of set functions. Although the necessity of this condition is not shown, we demonstrate by means of an example that the results cannot be improved upon in certain respects.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 3 , July 1958 , pp. 346 - 353
- Copyright
- Copyright © Cambridge Philosophical Society 1958
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