Ergodic decomposition of Dirichlet forms via direct integrals and applications Dello Schiavo, Lorenzo ; https://orcid.org/0000-0002-9881-6870 ddc:510 We study 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 σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique. Springer Nature 2023 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/10145 https://research-explorer.ista.ac.at/download/10145/14387 Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. 2023;58:573-615. doi:<a href="https://doi.org/10.1007/s11118-021-09951-y">10.1007/s11118-021-09951-y</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s11118-021-09951-y info:eu-repo/semantics/altIdentifier/issn/0926-2601 info:eu-repo/semantics/altIdentifier/e-issn/1572-929X info:eu-repo/semantics/altIdentifier/wos/000704213400001 info:eu-repo/semantics/altIdentifier/arxiv/2003.01366 info:eu-repo/semantics/openAccess