  Dependence is undoubtedly a central concept in statistics. Though, it proves
difficult to locate in the literature a formal definition which goes beyond the
self-evident 'dependence = non-independence'. This absence has allowed the term
'dependence' and its declination to be used vaguely and indiscriminately for
qualifying a variety of disparate notions, leading to numerous incongruities.
For example, the classical Pearson's, Spearman's or Kendall's correlations are
widely regarded as 'dependence measures' of major interest, in spite of
returning 0 in some cases of deterministic relationships between the variables
at play, evidently not measuring dependence at all. Arguing that research on
such a fundamental topic would benefit from a slightly more rigid framework,
this paper suggests a general definition of the dependence between two random
variables defined on the same probability space. Natural enough for aligning
with intuition, that definition is still sufficiently precise for allowing
unequivocal identification of a 'universal' representation of the dependence
structure of any bivariate distribution. Links between this representation and
familiar concepts are highlighted, and ultimately, the idea of a dependence
measure based on that universal representation is explored and shown to satisfy
Renyi's postulates.
