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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: [email protected]
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Abstract

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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

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