In the mathematical theory of free probability, the notion of free independence was introduced by Dan Voiculescu. The definition of free independence is parallel to the classical definition of independence, except that the role of Cartesian products of measure spaces (corresponding to tensor products of their function algebras) is played by the notion of a free product of (non-commutative) probability spaces. Let be a , i.e. a unital algebra over equipped with a unital linear functional . As an example, one could take, for a probability measure , Let be a family of unital subalgebras of .