  We study superpositions and direct integrals of quadratic and Dirichlet
forms. We show that each quasi-regular Dirichlet space over a probability space
admits a unique representation as a direct integral of irreducible Dirichlet
spaces, quasi-regular for the same underlying topology. The same holds for each
quasi-regular strongly local Dirichlet space over a metrizable Luzin, Radon
measure space, and admitting carr\'e du champ operator. In this case, the
representation is only projectively unique.
