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Stieltjes-type integrals

Published online by Cambridge University Press:  09 April 2009

A. M. Russell
A. M. Russell
Affiliation:
Department of Mathematics, University of MelbourneParkville 3052, Australia
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Burkill (1957) introduced extended Riemann-Stieltjes integrals of the form ∫baƒ(x)dkg(x)/dxk-1 to provide an alternative approach to the theory of distributions. We will denote Burkill's integral by (B)∫baƒ(x)dkg(x)/dxk-1 Burkill's paper (1957) partially motivated the study of the Riemann-Stieltjes integral in Russell (1970). He showed that the two integrals are not equivalent.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 4 , November 1975 , pp. 431 - 448
Copyright
Copyright © Australian Mathematical Society 1975

References

Bullen, P. S. (1971), ‘A criterion for n-convexity’, Pacific J. Math. 36, 81–98.CrossRefGoogle Scholar
Burkill, J. C. (1957), ‘An integral for distributions’, Proc. Cambridge Philos. Soc. 53, 821–824.CrossRefGoogle Scholar
Russell, A. M. (1970), ‘Functions of bounded second variation and Stieltjes-type integrals’, J. London Math. Soc. (2) 2, 193–208.CrossRefGoogle Scholar
Russell, A. M. (1973), ‘Functions of bounded kth variation’, Proc. London Math. Soc. (3) 26, 547–563.CrossRefGoogle Scholar
Webb, J. R. (1967), ‘A Hellinger integral representation for bounded linear functionls’, Pacific J. Math. 20, 327–337.CrossRefGoogle Scholar