Geodesic
Uniformly spread measures and vector fields
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 116-127

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We show that two different ideas of uniform spreading of locally finite measures on the $d$-dimensional Euclidean space are equivalent. The first idea is formulated in terms of finite distance transportations to the Lebesgue measure, while the second idea is formulated in terms of vector fields connecting a given measure with the Lebesgue measure. Bibl. – 11 titles. 
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     author = {M. Sodin and B. Tsirelson},
     title = {Uniformly spread measures and vector fields},
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     volume = {366},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a7/}
}
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M. Sodin; B. Tsirelson. Uniformly spread measures and vector fields. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 116-127. http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a7/