W 2 ( μ , ν ) := min γ ∈ Γ ( μ , ν ) ( ∫ | x 1 − x 2 | 2 d γ ( x 1 , x 2 ) ) 1 / 2 {\displaystyle W_{2}(\mu ,\nu ):=\min _{\gamma \in \Gamma (\mu ,\nu )}\left(\int |x_{1}-x_{2}|^{2}\,d\gamma (x_{1},x_{2})\right)^{1/2}}
w 2 2 ( μ , ν ) = inf ( μ ( t ) . ν ( t ) ) ∫ 0 1 | v ( , t ) | L 2 ( μ ( t ) ) 2 {\displaystyle w_{2}^{2}(\mu ,\nu )=\inf _{(\mu (t).\nu (t))}{\int _{0}^{1}}|v(,t)|_{L^{2}(\mu (t))}^{2}}
, 