Uniformly spread measures and vector fields

Mathematics – Classical Analysis and ODEs

Scientific paper

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11 pages

Scientific paper

We show that two different ideas of uniform spreading of locally finite
measures in 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.

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