# Optimal Transportation of Vector-Valued Measures

arXiv: https://arxiv.org/abs/1901.04765 · HTML: https://mlsanity.com/paper/1901.04765/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2019.

## Built on by (most cited first, 1 of 1)

- [Learning the temporal evolution of multivariate densities via normalizing flows](https://mlsanity.com/paper/2107.13735/) (2021)

## Abstract (arXiv)

Given two n-dimensional measures μ and nu on Polish spaces, we propose an optimal transportation's formulation, inspired by classical Kan-torovitch's formulation in the scalar case. In particular, we established a strong duality result and as a consequence, optimality conditions are investigated. Wasserstein's metrics induced by our formulation are also investigated.