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On the Existence of the Burkill Integral

Published online by Cambridge University Press:  20 November 2018

H. Kober
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The main problem of the present paper is the existence of the Burkill integral of an interval function ƒ(I) which is not supposed to be continuous. Little is known about this case, though otherwise the theory of the integral can be considered as complete: we may refer to Ringenberg's comprehensive paper (2) in which further references are given.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 115 - 121
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities (Cambridge, 1934).Google Scholar
2. Ringenberg, L. A., The theory of the Burkill integral, Duke Math. J., 15 (1948), 239-270.Google Scholar
3. Saks, S., Theory of the Integral(2nd revised ed., New York).Google Scholar