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An induction proof of the generalized Blaschke-Petkantschin formula
Published online by Cambridge University Press: 01 July 2016
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
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- Copyright
- Copyright © Applied Probability Trust 1996
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
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