Denjoy Integral Research Articles

On a constructive definition of the restricted Denjoy integral

where 9 is the set of partitions of J and I P I is the norm of P. The Burkill integral has been employed in a more general setting [1] to give a descriptive definition of the restricted Denjoy integral of point functions f. In this paper we show how this integral can be used to give a constructive definition of the restricted Denjoy integral and compare the classical construction with ours. We adopt the convention that I and J, with or without subscripts or superscripts, always denote a closed interval. Before we begin our discussion, let us recall the classical constructive definition ([2], 255-259) of the restricted Denjoy integral. Let T be a real-valued function whose domain, dom T, is a set of ordered pairs {(f, J)}, where f is a real-valued point function defined on J. The set

On the approximately continuous Denjoy integral

On the approximately continuous Denjoy integral

Věta o substituci pro Denjoyovy integrály

Věta o substituci pro Denjoyovy integrály

On Hobson's Convergence Theorem for Denjoy Integrals

Journal of the London Mathematical SocietyVolume s1-4, Issue 2 p. 127-132 Notes and Papers On Hobson's Convergence Theorem for Denjoy Integrals J. C. Burkill, J. C. BurkillSearch for more papers by this author J. C. Burkill, J. C. BurkillSearch for more papers by this author First published: April 1929 https://doi.org/10.1112/jlms/s1-4.14.127AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volumes1-4, Issue2April 1929Pages 127-132 RelatedInformation

Change of Variable in a Denjoy Integral

Journal of the London Mathematical SocietyVolume s1-4, Issue 1 p. 27-32 Notes and papers Change of Variable in a Denjoy Integral W. L. C. Sargent, W. L. C. SargentSearch for more papers by this author W. L. C. Sargent, W. L. C. SargentSearch for more papers by this author First published: January 1929 https://doi.org/10.1112/jlms/s1-4.1.27AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volumes1-4, Issue1January 1929Pages 27-32 RelatedInformation

Change of Variable in a Denjoy Integral

Change of Variable in a Denjoy Integral