@article{12104, abstract = {We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.}, author = {Dello Schiavo, Lorenzo and Wirth, Melchior}, issn = {1424-3202}, journal = {Journal of Evolution Equations}, number = {1}, publisher = {Springer Nature}, title = {{Ergodic decompositions of Dirichlet forms under order isomorphisms}}, doi = {10.1007/s00028-022-00859-7}, volume = {23}, year = {2023}, }