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On Multiple Integral Geometric Integrals and Their Applications to Probability Theory

Published online by Cambridge University Press:  20 November 2018

Franz Streit
Franz Streit*
Affiliation:
University of Toronto, Toronto, Ontario
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It has been pointed out repeatedly in the literature that the methods of integral geometry (a mathematical theory founded by Wilhelm Blaschke and considerably extended by several mathematicians) provide highly suitable means for the solution of problems concerning “geometrical probabilities“ [2; 6; 12; 15]. The possibilities for the application of these integral geometric results to the evaluation of probabilities, satisfying certain conditions of invariance with respect to a group of transformations which acts on the probability space, are obviously not yet exhausted. In this article, such applications are presented. First, some concepts and notation are introduced (§1). In the next section we derive some integral geometric relations (§ 2). These results are generalizations of known systems of formulae and they are valid in the k-dimensional Euclidean space. In § 3, we determine mean-value formulae for the fundamental characteristics of point-sets, generated by randomly placed convex bodies.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 151 - 163
Copyright
Copyright © Canadian Mathematical Society 1970

References

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