Talk:Lévy–Prokhorov metric

mistake on "Relation to other distances" section
The second bullet point apparently is wrong. I tried to find out that result in page 175 in Rachev and nothing similar seems to be there. Furthermore the probabilities \gamma=(1-\alpha) \delta_a+\alpha \delta_0$ with 0<a<\alpha<1,  and \delta_0  seem to provide a contradiction to such statement, since W_p(\gamma, \delta_0)^p=a^p\alpha and \pi(\gamma, \delta_0)=a, it is easy to find a, \alpha and p such that a^p\alpha-a^2<0, contradicting the statement. Luiscc1900 (talk) 16:57, 3 November 2022 (UTC)


 * I agree with this. I also checked the source and the cited inequality is nowhere to be seen! I am not 100% sure about the correctness of your counterexample (I think in the definition of $\gamma$ you need to swap $\alpha$ and $1-\alpha$ as weights), but I agree with the conclusion. 129.19.63.105 (talk) 20:33, 1 April 2024 (UTC)