Existence Conditions for the Lane Integral

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Dec 1967Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 18, page 1,067 (issn: 0002-9939,

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Authors: Smith, K. P.; Wright, F. M.;

doi: 10.2307/2035797 , 10.1090/s0002-9939-1967-0217235-4

Existence Conditions for the Lane Integral

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Abstract

If [a, b] is an interval of the real axis, and if G is a subset of [a, b] containing a and b, we use the terminology G-subdivision of [a, b] and G-refinement of a subdivision of [a, b] as in [1]. The concepts of singular graph, exceptional number, and summability set are as in [4]. If f and g are real-valued functions on an interval [a, b] of the real axis, and if there is a summability set G forf and g in [a, b], the Lane integral Lfafdg is the refinement limit

Keywords

differentiation and integration, measure theory

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