Let be non-empty, open and proper. This paper is concerned with , the space of -integrable Borel measures on equipped with the transportation metric introduced by Figalli and Gigli that allows the creation and destruction of mass on . Alternatively, we show that is isometric to a subset of Borel measures with the ordinary Wasserstein distance, on the one point completion of equipped with the shortcut metric In this article we construct bi-Lipschitz embeddings of the set of unordered -tuples in into Hilbert space. This generalises Almgren's bi-Lipschitz embedding theorem to the setting of optimal partial transport.
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| http://dx.doi.org/10.1007/s00208-024-02831-x | DOI Listing |
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Bi-Lipschitz embeddings of the space of unordered -tuples with a partial transportation metric.
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Let be non-empty, open and proper. This paper is concerned with , the space of -integrable Borel measures on equipped with the transportation metric introduced by Figalli and Gigli that allows the creation and destruction of mass on . Alternatively, we show that is isometric to a subset of Borel measures with the ordinary Wasserstein distance, on the one point completion of equipped with the shortcut metric In this article we construct bi-Lipschitz embeddings of the set of unordered -tuples in into Hilbert space.
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