  Since Pearson's correlation was introduced at the end of the 19th century
many dependence measures have appeared in the literature. Recently we have
suggested four simple axioms for dependence measures of random variables that
take values in Hilbert spaces. We showed that distance correlation satisfies
all these axioms. We still need a new measure of dependence because existing
measures either do not work in general metric spaces (that are not Hilbert
spaces) or they do not satisfy our four simple axioms. The earth mover's
correlation introduced in this paper applies in general metric spaces and
satisfies our four axioms (two of them in a weaker form).
