The multistochastic Monge–Kantorovich problem

The multistochastic Monge–Kantorovich problem on the product X = ∏ i = 1 n X i of n spaces is a generalization of the multimarginal Monge–Kantorovich problem. For a given integer number 1 ≤ k n we consider the minimization problem ∫ c d π → inf on the space of measures with fixed projections onto every X i 1 × … × X i k for arbitrary set of k indices { i 1 , … , i k } ⊂ { 1 , … , n } . In this paper we study basic properties of the multistochastic problem, including well-posedness, existence of a dual solution, boundedness and continuity of a dual solution.