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Abstract: We consider a lcsc group G acting properly on a Borel space S and measurablyon an underlying sigma-finite measure space. Our first main result is atransport formula connecting the Palm pairs of jointly stationary randommeasures on S. A key and new technical result is a measurable disintegrationof the Haar measure on G along the orbits. The second main result is anintrinsic characterization of the Palm pairs of a G-invariant random measure.We then proceed with deriving a general version of the mass-transport principlefor possibly non-transitive and non-unimodular group operations first in adeterministic and then in its full probabilistic form.



Author: Daniel Gentner, Günter Last

Source: https://arxiv.org/



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