  We propose a local and general dependence quantifier between two random
variables $X$ and $Y$, which we call Local Lift Dependence Scale, that does not
assume any form of dependence (e.g., linear) between $X$ and $Y$, and is
defined for a large class of random variables, singular and absolutely
continuous w.r.t Lebesgue measure. We argue that this dependence scale is more
general and suitable to study variable dependence than other specific local
dependence quantifiers and global dependence coefficients, as the Mutual
Information. An outline of how this dependence scale may be useful in branches
of applied probability and topics for future research are presented.
