Borel Cross-Sections and Maximal Invariants
The Annals of Statistics · 1976 · Volume 4 · Issue 5
Abstract
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.
Keywords
28A50, 57E20, 62A05, Cross-section of orbits, disintegration of measure, maximal invariant
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