  This paper introduces max-characteristic functions (max-CFs), which are an
offspring of multivariate extreme-value theory. A max-CF characterizes the
distribution of a random vector in R^d , whose components are nonnegative and
have finite expectation. Pointwise convergence of max-CFs is shown to be
equivalent with convergence with respect to the Wasserstein metric. The space
of max-CFs is not closed in the sense of pointwise convergence. An inversion
formula for max-CFs is established.
