Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-06T04:26:30.078Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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