 Let formula_13 be a measurable space.The total variation distance between two (positive) measures μ and ν is then given by

Here the supremum is taken over "f" ranging over the set of all measurable functions from "X" to [−1, 1].This is in contrast, for example, to the Wasserstein metric, where the definition is of the same form, but the supremum is taken over "f" ranging over the set of measurable functions from "X" to [−1, 1] which have Lipschitz constant at most 1; and also in contrast to the Radon metric, where the supremum is taken over "f" ranging over the set of continuous functions from "X" to [−1, 1].