Decomposition Formulae for Dirichlet Forms and Their Corollaries

We provide decompositions of symmetric Dirichlet forms into recurrent and transient parts as well conservative dissipative parts, in the framework $$\sigma $$ -finite measure spaces. Combining both formulae, we write every form sum a recurrent, dissipative, transient-conservative forms. Besides, prove that Mosco convergence preserves invariant sets shares same invariants with its approximating $${\mathcal {E}}^{(t)}$$ {E}}^{(\beta )}$$ . Finally, show equivalence between conservativeness (resp. dissipativity) (reps. The elaborated results are enlightened by some examples.