Abstract
Let Ω ⊂ Rn be non-empty, open and proper. This paper is concerned with Wbp(Ω) , the space of p-integrable Borel measures on Ω equipped with the partial transportation metric introduced by Figalli and Gigli that allows the creation and destruction of mass on ∂Ω . Alternatively, we show that Wbp(Ω) is isometric to a subset of Borel measures with the ordinary Wasserstein distance, on the one point completion of Ω equipped with the shortcut metric [Formula: see text] In this article we construct bi-Lipschitz embeddings of the set of unordered m-tuples in Wbp(Ω) into Hilbert space. This generalises Almgren's bi-Lipschitz embedding theorem to the setting of optimal partial transport.