1 An Elementary Introduction to Monotone Transportation after
نویسنده
چکیده
We outline existence of the Brenier map. As an application we present simple proofs of the multiplicative form of the Brunn–Minkowski inequality and the Marton–Talagrand inequality. 1.
منابع مشابه
An Elementary Introduction to Monotone Transportation
Monge gave a number of examples to illustrate the difficulties of the problem. Plainly if arbitrary measures are allowed it may not be possible to transport at all. If μ is a single point mass and ν consists of two point masses, each with weight 1/2, then no map T can “split μ in half”. Where transportation maps do exist, there may be many different optimal ones, even for measures on the line. ...
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