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L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208.","external_id":{"isi":["001042025400001"]},"isi":1,"year":"2023","citation":{"ama":"Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. 2023;28:1-12. doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>","apa":"Dello Schiavo, L., &#38; Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>","ieee":"L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023.","chicago":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>.","short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12.","mla":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>.","ista":"Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12."},"date_updated":"2023-12-13T11:24:57Z","abstract":[{"lang":"eng","text":"We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes."}],"day":"05","doi":"10.1214/23-ECP528","file_date_updated":"2023-06-19T09:37:40Z","quality_controlled":"1","page":"1-12","article_type":"original","publisher":"Institute of Mathematical Statistics","author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"},{"first_name":"Eugene","last_name":"Lytvynov","full_name":"Lytvynov, Eugene"}],"scopus_import":"1","_id":"13145","intvolume":"        28","title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","date_created":"2023-06-18T22:00:48Z","department":[{"_id":"JaMa"}],"article_processing_charge":"No","publication_status":"published"},{"year":"2023","citation":{"apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9."},"date_updated":"2023-06-28T11:54:35Z","external_id":{"isi":["000906214600004"]},"isi":1,"day":"01","doi":"10.1007/s00028-022-00859-7","abstract":[{"lang":"eng","text":"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."}],"acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","volume":23,"ddc":["510"],"scopus_import":"1","_id":"12104","issue":"1","author":[{"last_name":"Dello Schiavo","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"first_name":"Melchior","last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2023-01-08T23:00:53Z","department":[{"_id":"JaMa"}],"publication_status":"published","intvolume":"        23","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","quality_controlled":"1","ec_funded":1,"file_date_updated":"2023-01-20T10:45:06Z","publisher":"Springer Nature","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2023-01-01T00:00:00Z","publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"oa":1,"file":[{"file_id":"12325","creator":"dernst","relation":"main_file","access_level":"open_access","success":1,"date_updated":"2023-01-20T10:45:06Z","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","content_type":"application/pdf","date_created":"2023-01-20T10:45:06Z","file_size":422612,"checksum":"1f34f3e2cb521033de6154f274ea3a4e"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","has_accepted_license":"1","publication":"Journal of Evolution Equations","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}],"oa_version":"Published Version","article_number":"9","month":"01","language":[{"iso":"eng"}]}]