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The topology of the space of Denjoy integrable functions

Published online by Cambridge University Press:  17 April 2009

Chew Tuan Seng  and
Lee Peng Yee
Chew Tuan Seng
Affiliation:
National University of Singapore, Department of Mathematics Kent Ridge, Singapore 0511, Republic of Singapore
Lee Peng Yee
Affiliation:
National University of Singapore, Department of Mathematics Kent Ridge, Singapore 0511, Republic of Singapore
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Abstract

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In this paper, the topology of the Denjoy space and characterisation of precompact sets in the Denjoy space are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 3 , December 1990 , pp. 517 - 524
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Chew, T.S., ‘Nonlinear Henstock-Kurzweil integrals and representation theorems’, SEA Bull. Math. 12 (1988), 97–108.Google Scholar
[2]Chew, T.S., ‘The superposition operators in the space of Henstock-Kurzweil integrable functions’, Real Analysis Symposium, (Coleraine, 1988).Google Scholar
[3]Köthe, G., Topological vector spaces I (Springer-Verlag, Berlin, Heidleberg, New York, 1969).Google Scholar
[4]Krasnoselskii, M.A., Integral operators in spaces of summable functions (Noordhoff, 1976).CrossRefGoogle Scholar
[5]Lee, P.Y. and Chew, T.S., ‘A better convergence theorem for Henstock integrals’, Bull. London Math. Soc. 17 (1985), 557–564.Google Scholar
[6]Lee, P.Y. and Chew, T.S., ‘A Riesz-type definition of the Denjoy integral’, Real Analysis Exchange 11 (1985/1986), 221–227.Google Scholar
[7]Lee, P.Y. and Chew, T.S., ‘On convergence theorems for the nonabsolute integrals’, Bull. Austral. Math. Soc. 34 (1986), 133–140.Google Scholar
[8]Lee, P.Y., Lanzhou lectures on Henstock integration (World Scientific, 1989).Google Scholar
[9]Nakanishi, S., ‘L'intégration de Denjoy et l'intégration au moyen des espaces rangés, I-IV’, Proc. Japan Acad. 32 (1956), 678–683; 33, (1957), 13–18, 265–270; 34 (1958), 96–101.Google Scholar
[10]Saks, S., Theory of the integral, 2nd ed (Warsaw, 1937).Google Scholar
[11]Sargent, W.L.C., ‘On some theorems of Hahn, Banach and Steinhaus’, J. London Math. Soc. 28 (1953), 438–451.CrossRefGoogle Scholar