Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications

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