Open Access
September, 1976 Borel Cross-Sections and Maximal Invariants
James V. Bondar
Ann. Statist. 4(5): 866-877 (September, 1976). DOI: 10.1214/aos/1176343585


A measurable cross-section for orbits of a sample space under a free (exact) transformation group is shown to exist under topological regularity conditions. This is used to represent the sample space as essentially the product of a maximal invariant and an equivariant part, which implies Stein's representation for the density of the maximal invariant.


Download Citation

James V. Bondar. "Borel Cross-Sections and Maximal Invariants." Ann. Statist. 4 (5) 866 - 877, September, 1976.


Published: September, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0345.62004
MathSciNet: MR474589
Digital Object Identifier: 10.1214/aos/1176343585

Primary: 62A05
Secondary: 28A50 , 57E20

Keywords: Cross-section of orbits , disintegration of measure , maximal invariant

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 5 • September, 1976
Back to Top