Geodesic
Generalized Riemann Integration and an Intrinsic Topology
Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 395-413

Voir la notice de l'article provenant de la source Cambridge University Press

In generalized Riemann integration theory it is becoming increasingly clear that a particular collection of sets has some properties of a topology; it is a useful topology when general requirements hold, and the present paper examines the background. Thomson [23, 24] altered my original theory of the variation and Riemann-type integration that has Lebesgue properties, defining the variation of a function of interval-point pairs over the whole of a space T by using partial divisions of T instead of divisions covering T entirely, and also defining a Lebesgue-type integral. His reason might have been that a decomposable division space seems impossible in a general compact or locally compact space. McGill mentioned this to me, and in [15] connected Thomson's setting with topological measure and Topsøfe [25], giving an interesting theorem on the variation of the limit of a monotone increasing generalized sequence of open sets. 
Henstock, Ralph. Generalized Riemann Integration and an Intrinsic Topology. Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 395-413. doi: 10.4153/CJM-1980-031-0
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