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Existence and uniqueness of monotone measure-preserving maps. (English) Zbl 0873.28009

The author proves existence and uniqueness of monotone measure-preserving maps. Furthermore, he gives an example in which existence and uniqueness fail, and an appendix containing a version of the implicit function theorem used in the proof of uniqueness; it applies to functions which, though not continuously differentiable, are differences of two convex functions.

MSC:

28D05 Measure-preserving transformations
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