Abstract
We give an elementary proof that the Wasserstein distances, which play a basic role in optimal transportation issues, turn some, spaces of probability measures into separable complete metric spaces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Ambrosio, N. Gigli, and G. Savaré. Gradient flows in metric spaces and in the spaces of probability measures. Birkhäuser, Basel, 2005.
F. Bolley. Applications du transport optimal à des problèmes de limites de champ moyen. Thèse de doctorat, Ecole Normale Supérieure de Lyon. Available at http://www.lsp.ups-tlse.fr/Fp/Bolley, 2005.
F. Bolley. Quantitative concentration inequalities on sample path space for mean field interaction. Preprint available at http://www.lsp.ups-tlse.fr/Fp/Bolley 2005.
S. T. Rachev. Probability metrics and the stability of stochastic models. John Wiley and Sons, Chichester, 1991.
S. T. Rachev and L. Rüschendorf. Mass transportation problems Vol I and II. Springer, New York, 1998.
C. Villani. Topics in optimal transportation, volume 58 of Grad. Stud. Math. AMS, Providence, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bolley, F. (2008). Separability and completeness for the Wasserstein distance. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-77913-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77912-4
Online ISBN: 978-3-540-77913-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)