Geodesic
The group of diffeomorphisms of the~half-line, and random Cantor sets
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 857-868

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A certain one-parameter family of measures is constructed on the space of closed totally disconnected subsets of the half-line without isolated points. It is shown that these measures are quasi-invariant with respect to the group of smooth diffeomorphisms of the half-line, and the Radon–Nikodym derivatives are explicitly computed. 
@article{SM_1996_187_6_a4,
     author = {Yu. A. Neretin},
     title = {The group of diffeomorphisms of the~half-line, and random {Cantor} sets},
     journal = {Sbornik. Mathematics},
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     number = {6},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_6_a4/}
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Yu. A. Neretin. The group of diffeomorphisms of the~half-line, and random Cantor sets. Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 857-868. http://geodesic.mathdoc.fr/item/SM_1996_187_6_a4/