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An induction proof of the generalized Blaschke-Petkantschin formula

Published online by Cambridge University Press:  01 July 2016

E. B. Vedel Jensen
E. B. Vedel Jensen*
Affiliation:
University of Aarhus
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Extract

The classical Blaschke-Petkanschin formula is a formula in integral geometry givmg a geometric measure decomposition of the q-fold product of Lebesgue measure. The original versions are due to Blaschke and Petkanschin in the 1930s. In Zähle (1990) and Jensen and Kiêu (1992), generalized versions have been derived, where Lebesgue measure is replaced by Hausdorff measure.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 334
Copyright
Copyright © Applied Probability Trust 1996 

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References

Jensen, Ε. B. V., and Kjêu, K. (1992) A new integral geometric formula of the Blaschke–Petkantschin type. Math. Nachr. 156, 57–74.CrossRefGoogle Scholar
Miles, R. E. (1971) Isotropic random simplices. Adv. Appl. Prob. 3, 353–382.Google Scholar
Møller, J., (1985) A simple derivation of a formula of Blaschke and Petkantschin. Research Reports 138. Department of Theoretical Statistics, University of Aarhus.Google Scholar
Zähle, M. (1990) A kinematic formula and moment measures of random sets. Math. Nachr. 149, 325–340.CrossRefGoogle Scholar