@MISC{_cyclicalmonotonicity, author = {}, title = {CYCLICAL MONOTONICITY AND THE ERGODIC THEOREM}, year = {} }
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Abstract
Abstract. It is well known that optimal transport plans are cyclically mono-tone. The reverse implication that cyclically monotone transport plans are optimal needs some assumptions and the proof is non-trivial even if the costs are given by the squared euclidean distance on Rn. We establish this result as a corollary to the ergodic theorem. 1.