New answers tagged wasserstein-distance
2
votes
Unique coupling
For two measurable sets $A,B$, let $p=\mu(A)$ and $q=\nu(B)$. Consider any coupling of a Bernoulli$(p)$ and a Bernoulli$(q)$, say, $C:\{0,1\}^2 \to [0,1]$. Then we can find a coupling $(X,Y)$ of $\mu$...
- 1,724
2
votes
Accepted
Unique coupling
The only way this can happen is the situation that you described, where at least one of the measures gives full measure to a single point. In fact, the proof below does not require the two Polish ...
- 23.2k
Top 50 recent answers are included