{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T23:30:14Z","timestamp":1725492614322},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540347767"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/3-540-34777-1_18","type":"book-chapter","created":{"date-parts":[[2007,10,7]],"date-time":"2007-10-07T17:48:30Z","timestamp":1191779310000},"page":"137-143","source":"Crossref","is-referenced-by-count":0,"title":["Optional Sampling Theorem and Representation of Set-Valued Amart"],"prefix":"10.1007","author":[{"given":"Shoumei","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Guan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"18_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0022-247X(65)90049-1","volume":"12","author":"R. Aumann","year":"1965","unstructured":"R. Aumann (1965). Integrals of set valued functions, J. Math. Anal. Appl. 12, 1\u201312.","journal-title":"J. Math. Anal. Appl"},{"key":"18_CR2","first-page":"313","volume":"21","author":"S. Bagchi","year":"1985","unstructured":"S. Bagchi (1985). On a.s. convergence of classes of multivalued asymptotic martingales, Ann. Inst. H. Poincar\u00e9, Probabilit\u00e9s et Statistiques, 21, 313\u2013321.","journal-title":"Ann. Inst. H. Poincar\u00e9, Probabilit\u00e9s et Statistiques"},{"key":"18_CR3","doi-asserted-by":"crossref","unstructured":"G. Beer (1993). Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-8149-3"},{"key":"18_CR4","doi-asserted-by":"crossref","unstructured":"A. Bellow (1978). Some aspects of the theory of the vector-valued amarts, \u201cVector Space Measure and Applications I\u201d (ed. R. Aron and S. Dineen), Lect. Notes Math., 644, 57\u201367.","DOI":"10.1007\/BFb0066839"},{"key":"18_CR5","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF00534238","volume":"41","author":"A. Bellow","year":"1978","unstructured":"A. Bellow (1978). Uniform amarts: A class of asymptotic martingales for which strong almost sure convergence obtains. Z. Wahr. verw. Gebiete, 41, 177\u2013191.","journal-title":"Z. Wahr. verw. Gebiete"},{"key":"18_CR6","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/BF00539861","volume":"33","author":"R.V. Chacon","year":"1975","unstructured":"R.V. Chacon and L. Sucheston (1975). On convergence of vector-valued asymptotic martingales. Z. Wahr. verw. Gebiete. 33, 55\u201359.","journal-title":"Z. Wahr. verw. Gebiete"},{"key":"18_CR7","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/0047-259X(76)90031-2","volume":"6","author":"G.A. Edgar","year":"1976","unstructured":"G.A. Edgar and L. Suchistion (1976). Amarts: A class of asympotic martingales B. Discrete parameter. J. Multiv. Anal., 6, 193\u2013221.","journal-title":"J. Multiv. Anal."},{"key":"18_CR8","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1016\/0047-259X(76)90005-1","volume":"6","author":"G.A. Edgar","year":"1976","unstructured":"G.A. Edgar and L. Suchistion (1976). Amarts: A class of asympotic martingales A. continuous parameter. J. Multiv. Anal., 6, 572\u2013591.","journal-title":"J. Multiv. Anal."},{"key":"18_CR9","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/BF00533211","volume":"36","author":"G.A. Edgar","year":"1976","unstructured":"G.A. Edgar and L. Suchistion (1976). The Riesz decomposition for vectorvalued amarts, Z. Wahr. verw. Gebiete. 36, 85\u201392.","journal-title":"Z. Wahr. verw. Gebiete"},{"key":"18_CR10","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1016\/0022-247X(90)90275-K","volume":"153","author":"C. Hess","year":"1983","unstructured":"C. Hess (1983). Measurability and integrability of the weak upper limit of a sequence of multifunctions, J. Math. Anal. Appl., 153, 226\u2013249.","journal-title":"J. Math. Anal. Appl."},{"key":"18_CR11","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/0047-259X(77)90037-9","volume":"7","author":"F. Hiai","year":"1977","unstructured":"F. Hiai and H. Umegaki (1977). Integrals, conditional expectations and martingales of multivalued functions, Jour. Multiv. Anal., 7 149\u2013182.","journal-title":"Jour. Multiv. Anal."},{"key":"18_CR12","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1080\/07362998508809072","volume":"3","author":"A. Korvin de","year":"1985","unstructured":"A. de Korvin and R. Kleyle (1985). A convergence theorem for convex set valued supermartingales. Stoch. Anal. Appl., 3, 433\u2013445.","journal-title":"Stoch. Anal. Appl."},{"key":"18_CR13","doi-asserted-by":"publisher","first-page":"1384","DOI":"10.1214\/aop\/1022855757","volume":"26","author":"S. Li","year":"1998","unstructured":"S. Li and Y. Ogura (1998). Convergence of set valued sub-supermartingales in the Kuratowski-Mosco sense, Ann. Probab., 26, 1384\u20131402.","journal-title":"Ann. Probab."},{"key":"18_CR14","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1016\/S0165-0114(97)00092-4","volume":"101","author":"S. Li","year":"1999","unstructured":"S. Li and Y. Ogura (1999). Convergence of set valued and fuzzy valued martingals. Fuzzy Sets and Syst., 101, 453\u2013461.","journal-title":"Fuzzy Sets and Syst."},{"key":"18_CR15","doi-asserted-by":"crossref","unstructured":"S. Li, Y. Ogura and V. Kreinovich (2002). Limit Theorems and Applications of Set-Valued and Fuzzy Sets-Valued Random Variables, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-9932-0"},{"key":"18_CR16","first-page":"29","volume":"6","author":"D.Q. Luu","year":"1981","unstructured":"D.Q. Luu (1981). Representations and regularity of multivalued martingales, Acta Math. Vietn., 6, 29\u201340.","journal-title":"Acta Math. Vietn."},{"key":"18_CR17","doi-asserted-by":"crossref","first-page":"101","DOI":"10.7146\/math.scand.a-12044","volume":"54","author":"D.Q. Luu","year":"1984","unstructured":"D.Q. Luu (1984). Applications of set-valued Randon-Nikodym theorms to convergence of multivalued L 1-amarts, Math. Scand., 54, 101\u2013114.","journal-title":"Math. Scand."},{"key":"18_CR18","first-page":"63","volume":"300","author":"D.Q. Luu","year":"1985","unstructured":"D.Q. Luu (1985). Quelques resultats des amarts uniform nultivoques dans les espaces de Banach, CRAS, Paris, 300, 63\u201365.","journal-title":"CRAS, Paris"},{"key":"18_CR19","doi-asserted-by":"crossref","first-page":"5","DOI":"10.7146\/math.scand.a-12125","volume":"58","author":"D.Q. Luu","year":"1986","unstructured":"D.Q. Luu (1986). Representation theorems for multi-valued (regular) L 1- amarts, Math. Scand., 58, 5\u201322.","journal-title":"Math. Scand."},{"key":"18_CR20","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/0047-259X(85)90078-8","volume":"17","author":"N.S. Papageorgiou","year":"1985","unstructured":"N.S. Papageorgiou (1985). On the theorey of Banach space valued multifunctions. 1. integration and conditional wxpectation, J. Multiv. Anal., 17, 185\u2013206.","journal-title":"J. Multiv. Anal."},{"key":"18_CR21","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/0047-259X(85)90079-X","volume":"17","author":"N.S. Papageorgiou","year":"1987","unstructured":"N.S. Papageorgiou (1987). A convergence theorem for set valued multifunctions. 2. set valued martingales and set valued measures, J. Multiv. Anal., 17, 207\u2013227.","journal-title":"J. Multiv. Anal."},{"key":"18_CR22","doi-asserted-by":"publisher","first-page":"2495","DOI":"10.2307\/2154834","volume":"347","author":"N.S. Papageorgiou","year":"1995","unstructured":"N.S. Papageorgiou (1995). On the conditional expectation and convergence properties of random sets. Trans. Amer. Math. Soc., 347, 2495\u20132515.","journal-title":"Trans. Amer. Math. Soc."},{"key":"18_CR23","unstructured":"W.X. Zhang, Z.P. Wang and Y. Gao (1996). Set-valued random processes, Science Publisher. (in Chinese)."},{"key":"18_CR24","doi-asserted-by":"publisher","first-page":"807","DOI":"10.2307\/2154584","volume":"341","author":"Z.P. Wang","year":"1994","unstructured":"Z.P. Wang and X. Xue (1994). On convergence and closedness of multivalued martingales, Trans. Ameri. Math. Soc., 341, 807\u2013827.","journal-title":"Trans. Ameri. Math. Soc."}],"container-title":["Advances in Soft Computing","Soft Methods for Integrated Uncertainty Modelling"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-34777-1_18.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T21:24:56Z","timestamp":1619558696000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-34777-1_18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540347767"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/3-540-34777-1_18","relation":{},"subject":[]}}