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Jul 23, 2014 at 18:09 comment added Benoît Kloeckner You will find definition of the monotone rearrangement in many books on optimal transportation (e.g. one of Villani's books). In words, it is the measure on $[0,+\infty)^2$ that has marginals $\mu$ and $\mu^*$, and which ``maps'' the leftmost part of the mass of $\mu$ to the leftmost part of the mass of $\mu^*$.
Jul 23, 2014 at 17:09 vote accept Henry
Jul 23, 2014 at 17:09 comment added Henry I am not familiar with the monotone rearrangement from μ to μ ∗ and I could not find an explicit definition. Would you mind adding such details, please?
Jun 30, 2014 at 20:19 history answered Benoît Kloeckner CC BY-SA 3.0