Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-08-04T08:32:37.132Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of upper semicontinuously integrable functions

Part of: Real functions

Published online by Cambridge University Press:  09 April 2009

Zoltán Buczolich
Zoltán Buczolich
Affiliation:
Department of Analysis, Eötövos Loránd University, Budapest, Muzeum krt 6–8, Hungary, H-1088, e-mail: buczo@konig.elte.hu
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.

We show that for a Henstock-Kurzweil integrable function f for every ∈ > 0 one can choose an upper semicontinuous gage function δ, used in the definition of the HK-integral if and only if |f| is bounded by a Baire 1 function. This answers a question raised by C. E. Weil.

MSC classification

Secondary: 26A39: Denjoy and Perron integrals, other special integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 2 , October 1995 , pp. 244 - 254
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Alexandroff, P. and Hopf, H., Topologie (Chelsea, New York, 1965).Google Scholar
[2]Buczolich, Z., ‘Nearly upper semicontinuous gage functions in Rm’, Real Anal. Exchange 13 (1987–1988), 245–252.CrossRefGoogle Scholar
[3]Pfeffer, W. F., ‘A note on the generalized Riemann integral’, Proc. Amer. Math. Soc. 103 (1988), 1161–1166.CrossRefGoogle Scholar
[4]Pfeffer, W. F., ‘A Riemann type integration and the fundamental theorem of calculus’, Rend. Circolo Mat. Palermo (2), XXXVI (1987), 482–506.CrossRefGoogle Scholar
[5]Pfeffer, W. F., ‘Lectures on geometric integration and the divergence theorem’, Rend. Istit. Mat. Univ. Trieste, in press.Google Scholar
[6]Ziemer, W. P., Weakly differentiable functions (Springer, Berlin, 1989).CrossRefGoogle Scholar