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In this paper we show that we can use Markov kernels as a model for optimaltransport. This new framework can be easily translated into the standardcoupling formulation of optimal transport, and we show that we can use acoupling as a Markov kernel for many optimal transport problems. Using kernelsallows us to extend optimal transport to signed measures and treats the supportof the measure as the salient feature. This approach reveals additionalstructure for one-dimensional signed optimal transport.

Markov Kernels in Optimal Transport via Extending c-Cyclic Monotonicity