Geodesic
Quasi-invariant measures for topological dynamical systems
Izvestiya. Mathematics , Tome 8 (1974) no. 6, pp. 1287-1304.

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It is proved that for a topological dynamical system to admit an ergodic quasi-invariant measure of type III (a measure which is not equivalent to any $\sigma$-finite invariant measure) it is necessary and sufficient that this system have a recurrent point. For systems with a recurrent point, it is shown that there exist a nondenumerable number of pairwise singular ergodic quasi-invariant measures of type III. 
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I. P. Kornfeld. Quasi-invariant measures for topological dynamical systems. Izvestiya. Mathematics , Tome 8 (1974) no. 6, pp. 1287-1304. http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a7/

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