Geodesic
Differentiation of n-Dimensional Additive Processes
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 749-768

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

Let n ≧ 1 be an integer and let R n be the usual n-dimensional real vector space, considered together with all its usual structure. The usual n-dimensional Lebesgue measure on R n is denoted by λ n . The positive cone of R n is R n + and the interior of R n + is Pn . Hence Pn is the set of vectors with strictly positive coordinates. A subset of R n is called an interval if it is the cartesian product of one dimensional bounded intervals. If a, b ∊ R n then [a, b] denotes the interval {u|a ≦ u ≦ b|. The closure of any interval I is of the form [a, b]; the initial point of I will be defined as the vector a. The class of all intervals contained in R n + is denoted by . Also, for each u ∊ P n , let be the set of all intervals that are contained in the interval [0, u] and that have non-empty interiors. Finally let en ∊ P n be the vector with all coordinates equal to 1. 
Akcoglu, M. A.; Junco, A. Del. Differentiation of n-Dimensional Additive Processes. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 749-768. doi: 10.4153/CJM-1981-057-2
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