 Thus, using the usual absolute value function as the distance function on formula_76, for any formula_80, the formula_81-Wasserstein distance between formula_82 and formula_83 is
By similar reasoning, if formula_72 and formula_73 are point masses located at points formula_74 and formula_75 in formula_89, and we use the usual Euclidean norm on formula_89 as the distance function, then

Let formula_92 and formula_93 be two non-degenerate Gaussian measures (i.e.normal distributions) on formula_94, with respective expected values formula_95 and formula_96 and symmetric positive semi-definite covariance matrices formula_97 and formula_98.Then, with respect to the usual Euclidean norm on formula_89, the 2-Wasserstein distance between formula_82 and formula_101 is
This result generalises the earlier example of the Wasserstein distance between two point masses (at least in the case formula_103), since a point mass can be regarded as a normal distribution with covariance matrix equal to zero, in which case the trace term disappears and only the term involving the Euclidean distance between the means remains.