article published yes György Pál Gehér author Tamás Titkos author Daniel Virosztek author 48DB45DA-F248-11E8-B48F-1D18A9856A870000-0003-1109-5511 LaEr department International IST Postdoc Fellowship Programme project The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0<p<∞ is any parameter value. Roughly speaking, we will prove that any isometric embedding can be described by a special kind of X×(0,1]-indexed family of nonnegative finite measures. Our result implies that a typical non-surjective isometric embedding of Wp(X) splits mass and does not preserve the shape of measures. In order to stress that the lack of surjectivity is what makes things challenging, we will prove alternatively that Wp(X) is isometrically rigid for all 0<p<∞. Elsevier2019 eng 0022-247X 1096-0813 1809.01101 00048656390003110.1016/j.jmaa.2019.123435 4802 G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019). Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. 2019;480(2). doi:<a href="https://doi.org/10.1016/j.jmaa.2019.123435">10.1016/j.jmaa.2019.123435</a> Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. Elsevier. <a href="https://doi.org/10.1016/j.jmaa.2019.123435">https://doi.org/10.1016/j.jmaa.2019.123435</a> Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>. Elsevier, 2019. <a href="https://doi.org/10.1016/j.jmaa.2019.123435">https://doi.org/10.1016/j.jmaa.2019.123435</a>. Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2, 123435, Elsevier, 2019, doi:<a href="https://doi.org/10.1016/j.jmaa.2019.123435">10.1016/j.jmaa.2019.123435</a>. G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2. Elsevier, 2019. Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2), 123435. 68432019-09-01T22:01:01Z2025-07-10T11:53:55Z