Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-09T13:30:56.738Z Has data issue: false hasContentIssue false
  • English
  • Français

On Convergence theorems for nonabsolute integrals

Published online by Cambridge University Press:  17 April 2009

Lee Peng Yee  and
Chew Tuan Seng
Lee Peng Yee
Affiliation:
National University of Singapore, Republic of Singapore
Chew Tuan Seng
Affiliation:
National University of Singapore, Republic of Singapore
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper the Perron integrability of the limit of a sequence of functions is proved under certain convergene conditions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 1 , August 1986 , pp. 133 - 140
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Burkill, J.C., “The approximately continuous Perron integral”, Math. Z. 34 (1931), 270–278.Google Scholar
[2]Celidze, V.G. and Džvaršeǐšvili, A.G., Theory of the Denjoy integral and some of its applications, in Russian, (Tbilisi, 1978).Google Scholar
[3]Džvaršeǐšvili, A.G., “On a sequence of integrals in the sense of Denjoy”, Akad. Nauk Gruzin. SSR. Trudy Mat. Inst. Rajmadze 18 (1951), 221–236.Google Scholar
[4]Henstock, R., Theory of integration, (London, 1963).Google Scholar
[5]Henstock, R., “A Riemann-type integral of Lebesgue power”, Canad. J. Math. 20 (1968), 79–87.CrossRefGoogle Scholar
[6]Yee, Lee Peng and Seng, Chew Tuan, “A better convergence theorem for Henstock integrals”, Bull. London Math. Soc. 17 (1985) 557–564.Google Scholar
[7]Yee, Lee Peng and Seng, Chew Tuan, “A Riesz-type definition of the Denjoy integral”, Real Anal. Exchange 11 (1985/1986) No.1, 221–227.Google Scholar
[8]Saks, S., Theory of the integral, 2nd ed., (Warsaw, 1937).Google Scholar