Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T04:28:24.045Z Has data issue: false hasContentIssue false
  • English
  • Français

On the generalised dominated convergence theorem

Published online by Cambridge University Press:  17 April 2009

Chew Tuan Seng
Chew Tuan Seng
Affiliation:
National University of Singapore, Department of Mathematics, Lower Kent Ridge Road, Singapore 0511, 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 we give another version of the generalised dominated convergence theorem, which is better than other convergence theorems for Perron integrals in the sense that it can be applied more easily.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 2 , April 1988 , pp. 165 - 171
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Alexiewicz, A., ‘Linear functionals on Denjoy-integrable functions’, Colloq. Math. 1 (1948), 289–293.CrossRefGoogle Scholar
[2]Djvarsheishvili, 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
[3]Peng Yee, Lee and Tuan Seng, Chew, ‘A better convergence theorem for Henstock integrals’, Bull London Math. Soc. 17 (1985), 557–564.Google Scholar
[4]Yee, Lee Peng and Seng, Chew Tuan, ‘A Riesz-type definition of the Denjoy integral’, Real Anal. Exchange 11 (1985/1986), 221–227.CrossRefGoogle Scholar
[5]Peng Yee, Lee and Tuan Seng, Chew, ‘On Convergence theorems for the nonabsolute integrals’, Bull. Austral. Math. Soc. 34 (1986), 133–140.Google Scholar
[6]Peng Yee, Lee and Tuan Seng, Chew, ‘A short proof of the controlled convergence theorem for Henstock iiitegrals’, Bull. London Math. Soc. 19 (1987), 60–62.Google Scholar
[7]Ke-cheng, Liao, ‘A refinement of the controlled convergence theorem for Henstock integrals’, South East Asian Bull. Math. 11 (1987). No 1.Google Scholar
[8]Saks, S., ‘Theory of the integral’.Google Scholar
[9]Sargent, W.L., ‘On linear functions in spaces of conditionally integrable functions’, Quart. J. Math. Oxford Ser. (2) 1 (1950), 288–298.CrossRefGoogle Scholar