Does 1-Wasserstein metric have bounds?

jer

New Member
#1
Given \( l_1(u,v)=\int_{-\infty}^{+\infty}|U-V| \) the 1-Wasserstein distance with \(u\) and \(v\) two probability distributions and \(U\) and \(V\) their respective CDFs. The values of \(u\) and \(v\) are all positive in my case.

Let's assume that I have already computed \(a=max(u)\), \(b=max(v)\), \(c=min(u)\), and \(d=min(v)\),
Does \( l_1 \)have an upper and a lower bound?