Geodesic
Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group
Sbornik. Mathematics, Tome 205 (2014) no. 2, pp. 192-219 Cet article a éte moissonné depuis la source Math-Net.Ru

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The aim of this paper is to prove ergodic decomposition theorems for probability measures which are quasi-invariant under Borel actions of inductively compact groups as well as for $\sigma$-finite invariant measures. For infinite measures the ergodic decomposition is not unique, but the measure class of the decomposing measure on the space of projective measures is uniquely defined by the initial invariant measure. Bibliography: 21 titles.
Keywords: ergodic decomposition, infinite-dimensional groups, quasi-invariant measure, infinite-dimensional unitary group, measurable decomposition. 
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A. I. Bufetov. Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group. Sbornik. Mathematics, Tome 205 (2014) no. 2, pp. 192-219. http://geodesic.mathdoc.fr/item/SM_2014_205_2_a1/

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