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On the Lower Derivate of a Set Function

Published online by Cambridge University Press:  20 November 2018

W. F. Pfeffer
W. F. Pfeffer*
Affiliation:
University of California, Davis, California
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In (5), the following theorem was proved in a very general setting:

(1) An additive set function is non-negative whenever its lower derivative is non-negative.

For a continuous additive function of intervals, theorem (1) can be improved as follows:

(2) A continuous additive set function is non-negative whenever its lower derivative is non-negative except, perhaps, on a countable set.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1489 - 1498
Copyright
Copyright © Canadian Mathematical Society 1968

References

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