An Elementary Introduction to Monotone Transportation
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چکیده
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. If μ consists of two equal masses at (say) 0 and 1, and ν consists of two equal masses at 2 and 3 then it does not matter whether we choose
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تاریخ انتشار 2004