Geodesic
Derivatives and Integrals with Respect to a Base Function of Generalized Bounded Variation
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 225-241

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In this paper we consider measures determined by arbitrary functions G(x) for which finite right and left limits exist everywhere and indicate how some of these measures permit the definition of generalized integrals of constructive or Denjoy type. These definitions are related to corresponding descriptive definitions based on the Perron approach as given by Ward (6) and Henstock (2). An exposition of the introductory theory is given in (1). 
Ellis, H. W.; Jeffery, R. L. Derivatives and Integrals with Respect to a Base Function of Generalized Bounded Variation. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 225-241. doi: 10.4153/CJM-1967-015-6
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[1] 1. Ellis, H. W. and Jeffery, R. L., On measures determined by functions with finite right and left limits everywhere, submitted to Can. Math. Bull. Google Scholar

[2] 2. Henstock, R., A new descriptive definition of the Ward integral, J. London Math. Soc., 35 (1960), 43–48. Google Scholar

[3] 3. Henstock, R., N-variation, and N-variational integrals of set functions, Proc. London Math. Soc., 36 (1961), 109–132. Google Scholar

[4] 4. Jeffery, R. L., Theory of functions of a real variable, 2nd ed. (Toronto, 1953). Google Scholar

[5] 5. Munroe, M. E., Introduction to measure and integration (New York, 1953). Google Scholar

[6] 6. Ward, A. J., The Perron-Stieltjes integral, Math. Z., 41 (1936), 578–604. Google Scholar

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