Measures of the functional dependence of random vectors

•The measure of functional dependence for random vectors is proposed.•Calculated examples related to this measure are provided.•Some basic properties of this measure are proved and discussed.

In this work, we define a set of properties that any measure of functional dependence that exists between random vectors should possess. We also construct measures of functional dependence and show that they satisfy the properties mentioned above. Relationships between these measures and previously defined measures of functional dependence between random variables are discussed.