Geodesic
An Approximately Continuous Perron Integral
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 261-263

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J. C. Burkill [1] has defined the AP-integral whose indefinite integral is approximately continuous. An (approximately continuous) function which is approximately derivable at all points of an interval is necessarily an indefinite AP-integral of its approximate derivative. 
Kubota, Y. An Approximately Continuous Perron Integral. Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 261-263. doi: 10.4153/CMB-1971-048-0
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[1] 1. Burkill, J. C., The approximately continuous Perron integral. Math. Z. 34 (1931), 270-278 Google Scholar

[2] 2. Burkill, J. C., Integrals and trigonometric series, Proc. London Math. Soc. (3) 1 (1951), 46-57. Google Scholar

[3] 3. Goffman, C. and Neugerbauer, C. J., On approximate derivatives, Canad. J. Math. 11 (1960), 962-966. Google Scholar

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