Geodesic
Majorants in Variational Integration
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 49-74

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

In Perron integration, majorants are usually functions of points. If the domain of definition is a Euclidean space of n dimensions, we can define a finitely additive n-dimensional majorant rectangle function by taking suitable differences of the majorant point function with respect to each of the n coordinates. The way is then open to a generalization, in that we need only suppose that the majorant rectangle function is finitely superadditive. Similarly, we need only suppose that a minorant rectangle function is finitely subadditive. These kinds of rectangle functions were used by J. Mařík (5) to prove the Fubini theorem for Perron integrals in Euclidean space of m + n dimensions. He also proved that for a function that is Perron, and absolutely Perron, integrable, the majorant and minorant rectangle functions can be taken to be finitely additive. As a result he posed the following problem. 
Henstock, Ralph. Majorants in Variational Integration. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 49-74. doi: 10.4153/CJM-1966-008-9
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