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On functions of bounded ω-variation, II

Published online by Cambridge University Press:  09 April 2009

P. C. Bhakta
P. C. Bhakta
Affiliation:
Department of Mathematics, The University of Burdwan, Burdwan, West Bengal, India
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Let ω(x) be a non-decreasing function defined in the interval [a, b]. We extend the definition to all x by taking ω(x) = ω(a) for x < a and ω(x) = ω(b) for x > b. R. L. Jeffery [2] has denoted by the class of functions F(x) defined as follows:

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 3 , August 1965 , pp. 380 - 387
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Bhakta, P. C., On functions of bounded ω-variation. Communicated to ‘Rivista di Matematica della University Parma’ for publication.Google Scholar
[2]Jeffery, R. L., Generalised integrals with respect to functions of bounded variation, Can. J. Math. 10 (1958) 617–628.Google Scholar
[3]Kennedy, M. D., Upper and lower Lebesgue integrals, Proc. Lond. Math. Soc. (2) 32 (1930–1931), 21–50.Google Scholar
[4]Natanson, I. P., Theory of functions of a real variable (New York, 1955), p.205.Google Scholar