Palm pairs and the general mass-transport principle

Details Palm pairs and the general mass-transport principle Palm pairs and the general mass-transport principle

2009-01-31

arxiv.org/abs/0902.0068v2

a revised version will be published in Math. Z. (2010)

Mathematics

Probability

26 pages

Scientific paper

10.1007/s00209-009-0642-4

We consider a lcsc group G acting properly on a Borel space S and measurably on an underlying sigma-finite measure space. Our first main result is a transport formula connecting the Palm pairs of jointly stationary random measures on S. A key (and new) technical result is a measurable disintegration of the Haar measure on G along the orbits. The second main result is an intrinsic characterization of the Palm pairs of a G-invariant random measure. We then proceed with deriving a general version of the mass-transport principle for possibly non-transitive and non-unimodular group operations first in a deterministic and then in its full probabilistic form.

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