Real Analysis Exchange
- Real Anal. Exchange
- Volume 41, Number 1 (2016), 173-226.
On VBG Functions and the Denjoy-Khintchine Integral
The study of functions of generalized bounded variation (VBG) and generalized absolute continuity (ACG) that appears in Saks’s treatise Theory of the Integral can be thoroughly reworked by using some aspects of the theory of variational measures proposed originally by Ralph Henstock and extended by many others. We present a development of these concepts and use it for a characterization of the Denjoy-Khintchine integral.
Real Anal. Exchange, Volume 41, Number 1 (2016), 173-226.
First available in Project Euclid: 29 March 2017
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 26A39: Denjoy and Perron integrals, other special integrals 26A45.
Thomson, Brian S. On VBG Functions and the Denjoy-Khintchine Integral. Real Anal. Exchange 41 (2016), no. 1, 173--226. https://projecteuclid.org/euclid.rae/1490752823