The Wasserstein Distance and its Behaviour along Geodesics
In this chapter we will introduce the p-th Wasserstein distance W p (μ, ν) between two measures μ, ν ∈ Open image in new window (X). The first section is devoted to its preliminary properties, in connection with the optimal transportation problems studied in the previous chapter and with narrow convergence: the main topological results are valid in general metric spaces.
KeywordsHilbert Space Constant Speed Polish Space Optimal Plan Convex Banach Space
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