Measure of complete dependence of random vectors

•We construct a family of marginal-free measures of dependence between random vectors.•We prove that these measures are maximized when the one random vector is a measurable function of another.•We also prove several other basic properties of these measures.

In this work, we define a family of measures of complete dependence of absolutely continuous random vectors extended those of random variables. We show that these measures satisfy a suitable set of properties to be called measures of complete dependence. Computational examples are also given.