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On Ward's Perron-Stieltjes Integral
Published online by Cambridge University Press: 20 November 2018
Extract
In the paper (5), Ward defines an integral of Perron type of a finite function f with respect to another finite function g, where g need not be of bounded variation. There arise two problems, (a) and (b) below, that have not been dealt with in (5).
If f = j at a countable number of points everywhere dense in (a, b), where f and j are both integrable with respect to g, then f — j can be nonzero on a large set of points of (a, b).
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- Copyright © Canadian Mathematical Society 1957
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