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Differentiation of n-Dimensional Additive Processes

Published online by Cambridge University Press:  20 November 2018

M. A. Akcoglu  and
A. Del Junco
M. A. Akcoglu
Affiliation:
University of Toronto, Toronto, Ontario
A. Del Junco
Affiliation:
Ohio State University, Columbus, Ohio
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Let n ≧ 1 be an integer and let Rn be the usual n-dimensional real vector space, considered together with all its usual structure. The usual n-dimensional Lebesgue measure on Rn is denoted by λn. The positive cone of Rn is Rn+ and the interior of Rn + is Pn. Hence Pn is the set of vectors with strictly positive coordinates. A subset of Rn is called an interval if it is the cartesian product of one dimensional bounded intervals. If a, b ∊ Rn 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 Rn+ is denoted by . Also, for each u ∊ Pn, let be the set of all intervals that are contained in the interval [0, u] and that have non-empty interiors. Finally let en ∊ Pn be the vector with all coordinates equal to 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 3 , 01 June 1981 , pp. 749 - 768
Copyright
Copyright © Canadian Mathematical Society 1981

References

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