{"id":"https://openalex.org/W2070648893","doi":"https://doi.org/10.1109/tit.1974.1055287","title":"The ergodic decomposition of stationary discrete random processes","display_name":"The ergodic decomposition of stationary discrete random processes","publication_year":1974,"publication_date":"1974-09-01","ids":{"openalex":"https://openalex.org/W2070648893","doi":"https://doi.org/10.1109/tit.1974.1055287","mag":"2070648893"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1974.1055287","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1974.1055287","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061042317","display_name":"Robert M. Gray","orcid":"https://orcid.org/0000-0002-6947-3637"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Gray","raw_affiliation_strings":["Electrical Engineering Department, University of Stanford, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068322739","display_name":"L. Davisson","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Davisson","raw_affiliation_strings":["Electrical Engineering Department, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.8405,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.97289612,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"20","issue":"5","first_page":"625","last_page":"636"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.8773292899131775},{"id":"https://openalex.org/keywords/stationary-ergodic-process","display_name":"Stationary ergodic process","score":0.693218469619751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6546149253845215},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5474085211753845},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5169153213500977},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.4712410569190979},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4460502564907074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44236430525779724},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4295557737350464},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4281969666481018},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24801215529441833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23994073271751404},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09956461191177368},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.09179648756980896}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.8773292899131775},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.693218469619751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6546149253845215},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5474085211753845},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5169153213500977},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.4712410569190979},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4460502564907074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44236430525779724},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4295557737350464},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4281969666481018},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24801215529441833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23994073271751404},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09956461191177368},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.09179648756980896},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1974.1055287","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1974.1055287","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6600000262260437,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1489735312","https://openalex.org/W1968250327","https://openalex.org/W1983537136","https://openalex.org/W1989008275","https://openalex.org/W2029071561","https://openalex.org/W2048692459","https://openalex.org/W2051625847","https://openalex.org/W2087171258","https://openalex.org/W2115468292","https://openalex.org/W2131024393","https://openalex.org/W2141463438","https://openalex.org/W2142901448","https://openalex.org/W2160646668","https://openalex.org/W2319450871","https://openalex.org/W2324610639","https://openalex.org/W2802739963","https://openalex.org/W4234225207","https://openalex.org/W4255034261"],"related_works":["https://openalex.org/W2341040961","https://openalex.org/W4292101436","https://openalex.org/W73641039","https://openalex.org/W1043977585","https://openalex.org/W4249362165","https://openalex.org/W2040159604","https://openalex.org/W4239611712","https://openalex.org/W2616954029","https://openalex.org/W4249115484","https://openalex.org/W1190143688"],"abstract_inverted_index":{"The":[0,32],"ergodic":[1],"decomposition":[2],"is":[3,19,34,46],"discussed,":[4],"and":[5,43,49,52,57,69],"a":[6,71],"version":[7],"focusing":[8],"on":[9],"the":[10,22,40,44],"structure":[11],"of":[12,16,25],"individual":[13],"sample":[14],"functions":[15],"stationary":[17],"processes":[18,28],"proved":[20],"for":[21,63],"special":[23],"case":[24,38],"discrete-time":[26],"random":[27],"with":[29,70],"discrete":[30],"alphabets.":[31],"result":[33],"stronger":[35],"in":[36],"this":[37],"than":[39],"usual":[41],"theorem,":[42],"proof":[45],"both":[47,67],"intuitive":[48],"simple.":[50],"Estimation-theoretic":[51],"information-theoretic":[53],"interpretations":[54],"are":[55],"developed":[56],"applied":[58],"to":[59],"prove":[60],"existence":[61],"theorems":[62],"universal":[64],"source":[65],"codes,":[66],"noiseless":[68],"fidelity":[72],"criterion.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}