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On the Lower Derivate of a Set Function
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1968
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