[{"citation":{"lncs":" Ahlswede, R.: The final form of Tao's inequality relating conditional expectation and conditional mutual information. ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 1, 239-242 (2007).","wels":"Ahlswede, R. (2007): The final form of Tao's inequality relating conditional expectation and conditional mutual information *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*,1:(2): 239-242.","ieee":" R. Ahlswede, “The final form of Tao's inequality relating conditional expectation and conditional mutual information”, *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, vol. 1, 2007, pp. 239-242.","dgps":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, *1*(2), 239-242. AMER INST MATHEMATICAL SCIENCES. doi:10.3934/amc.2007.1.239.

","chicago":"Ahlswede, Rudolf. 2007. “The final form of Tao's inequality relating conditional expectation and conditional mutual information”. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1 (2): 239-242.

","mla":"Ahlswede, Rudolf. “The final form of Tao's inequality relating conditional expectation and conditional mutual information”. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1.2 (2007): 239-242.","bio1":"Ahlswede R (2007)

The final form of Tao's inequality relating conditional expectation and conditional mutual information.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS 1(2): 239-242.","angewandte-chemie":"R. Ahlswede, “The final form of Tao's inequality relating conditional expectation and conditional mutual information”, *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, **2007**, *1*, 239-242.","harvard1":"Ahlswede, R., 2007. The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, 1(2), p 239-242.","frontiers":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1, 239-242.","default":"Ahlswede R (2007)

*ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1(2): 239-242.","apa_indent":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, *1*(2), 239-242. doi:10.3934/amc.2007.1.239

","apa":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, *1*(2), 239-242. doi:10.3934/amc.2007.1.239"},"isi":1,"_id":"1592060","intvolume":" 1","uri_base":"https://pub.uni-bielefeld.de","author":[{"id":"10479","last_name":"Ahlswede","full_name":"Ahlswede, Rudolf","first_name":"Rudolf"}],"message":"NEWISI20100428 NEW ISI record:\r\nDepartments: Univ Bielefeld, Dept Math, D-33501 Bielefeld, Germany.\r\nISI Id: ISI:000254707400004 / DOI erg., public gestellt (Rd, 30.4.19)","article_type":"original","publication_status":"published","status":"public","department":[{"_id":"10020","tree":[{"_id":"10020"}]}],"user_id":"67994","date_updated":"2019-04-30T14:25:05Z","publication_identifier":{"issn":[]},"external_id":{"isi":[]},"issue":"2","volume":1,"type":"journal_article","creator":{"login":"riedel","id":"67994"},"dini_type":"doc-type:article","page":"239-242","dc":{"subject":["arithmetic progressions","information theoretic methods for combinators and number theory","Pinsker inequality","regularity lemma"],"rights":["info:eu-repo/semantics/closedAccess"],"type":["info:eu-repo/semantics/article","doc-type:article","text"],"creator":["Ahlswede, Rudolf"],"date":["2007"],"description":["Recently Terence Tao approached Szemeredi's Regularity Lemma from the perspectives of Probability Theory and Information Theory instead of Graph Theory and found a stronger variant of this lemma, which involves a new parameter. To pass from an entropy formulation to an expectation formulation he found the following: Let Y, and X, X' be discrete random variables taking values in Y and X, respectively, where Y subset of [-1, 1], and with X' = f(X) for a (deterministic) function f. Then we have E(vertical bar E(Y vertical bar X') - E(Y vertical bar X)vertical bar) <= 2I(X Lambda Y vertical bar X')1/2. We show that the constant 2 can be improved to (2ln2)1/2 and that this is the best possible constant."],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.3934/amc.2007.1.239","info:eu-repo/semantics/altIdentifier/issn/1930-5346","info:eu-repo/semantics/altIdentifier/wos/000254707400004"],"identifier":["https://pub.uni-bielefeld.de/record/1592060"],"language":["eng"],"publisher":["AMER INST MATHEMATICAL SCIENCES"],"title":["The final form of Tao's inequality relating conditional expectation and conditional mutual information"],"source":["Ahlswede R. The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*. 2007;1(2):239-242."]},"abstract":[{"lang":"eng"}],"date_created":"2010-04-28T11:50:16Z","publication":"ADVANCES IN MATHEMATICS OF COMMUNICATIONS","language":[{}],"quality_controlled":"1","keyword":[]}]