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. 
@article{IM2_1974_8_6_a7,
     author = {I. P. Kornfeld},
     title = {Quasi-invariant measures for topological dynamical systems},
     journal = {Izvestiya. Mathematics },
     pages = {1287--1304},
     publisher = {mathdoc},
     volume = {8},
     number = {6},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a7/}
}
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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/