{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T03:15:22Z","timestamp":1787368522267,"version":"build-2736575974"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1991,12,1]],"date-time":"1991-12-01T00:00:00Z","timestamp":691545600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[1991,12]]},"DOI":"10.1007\/bf02204813","type":"journal-article","created":{"date-parts":[[2005,10,5]],"date-time":"2005-10-05T14:47:16Z","timestamp":1128523636000},"page":"115-156","source":"Crossref","is-referenced-by-count":11,"title":["Conditional expectation of integrands and random sets"],"prefix":"10.1007","volume":"30","author":[{"given":"A.","family":"Truffert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"BF02204813_CR1","doi-asserted-by":"crossref","unstructured":"Z. Arstein, Limit laws for multifunctions applied to an optimization problem, in:Proc. Catania Conf. on Multifunctions and Integrands ed. G. Salinetti, Lecture Notes in Mathematics 1901 (Springer, 1983) p. 66.","DOI":"10.1007\/BFb0098802"},{"key":"BF02204813_CR2","volume-title":"Proc. Conf. on Aspects of Mathematics and Applications","author":"H. Attough","year":"1986","unstructured":"H. Attough and H. Brezis, Duality for the sum of convex functions in general Banach spaces. in:Proc. Conf. on Aspects of Mathematics and Applications, ed. J.A. Barroso (Elsevier Science, Amsterdam, 1986)."},{"key":"BF02204813_CR3","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/0022-247X(73)90170-4","volume":"42","author":"J.M. Bismut","year":"1973","unstructured":"J.M. Bismut, Int\u00e9grales convexes et probabilit\u00e9s, J. Math. Anal. Appl. 42 (1973) 639.","journal-title":"J. Math. Anal. Appl."},{"key":"BF02204813_CR4","unstructured":"A. Bourass, Comparaison des fonctionnelles int\u00e9grales sur les s\u00e9lections d'une multiapplication mesurable (III). Conditions de crossance et semi-continuit\u00e9 forte et en mesure d'une fonctionnelle int\u00e9grale, Travaux du S\u00e9minaire Analyse Convexe de Montpellier 11 (1982)."},{"key":"BF02204813_CR5","unstructured":"A. Bourass and A. Truffert, Ensembles ferm\u00e9s d\u00e9composables dans les espaces int\u00e9graux de type Orlicz, Travaux du S\u00e9minaire Analyse Convexe de Montpellier 15 (1982)."},{"key":"BF02204813_CR6","volume-title":"Condition de croissance associ\u00e9e \u00e0 l'inclusion des sections (d'apr\u00e8s A. Foug\u00e8res-R. Vaudene)","author":"A. Bourass","year":"1983","unstructured":"A. Bourass and M. Valadier. Condition de croissance associ\u00e9e \u00e0 l'inclusion des sections (d'apr\u00e8s A. Foug\u00e8res-R. Vaudene) Working paper, AVAMAC, University of Perpignan, France (1983)."},{"key":"BF02204813_CR7","unstructured":"C. Castaing, Repr\u00e9sentation int\u00e9grale des multifonctions s\u00e9par\u00e9ment \u03c3-additives et s\u00e9par\u00e9ment continues. Travaux du S\u00e9minaire Analyse Convexe de Montpellier 18 (1984)."},{"key":"BF02204813_CR8","unstructured":"C. Castaing and P. Clauzure, Quelques r\u00e9sultats de repr\u00e9sentation int\u00e9grale et applications \u00e0 l'esp\u00e9rance conditionnelle des multi-applications et des int\u00e9grandes, Travaux du S\u00e9minaire Analyse Convexe de Montpellier 14 (1979)."},{"key":"BF02204813_CR9","doi-asserted-by":"crossref","unstructured":"C. Castaing and M. Valadier,Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580 (Springer, 1977).","DOI":"10.1007\/BFb0087685"},{"key":"BF02204813_CR10","first-page":"167","volume":"9","author":"J. P. Daur\u00e8s","year":"1973","unstructured":"J. P. Daur\u00e8s, Version multivoque du th\u00e9or\u00e8me de Doob, Ann. Inst. H. Poincar\u00e9, sect. B 9 (1973) 167.","journal-title":"Ann. Inst. H. Poincar\u00e9, sect. B"},{"key":"BF02204813_CR11","unstructured":"J.L. Doob,Stochastic Processes, (Wiley, 1953)."},{"key":"BF02204813_CR12","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1137\/1121037","volume":"21","author":"E.B. Dynkin","year":"1976","unstructured":"E.B. Dynkin and I.V. Evstigneev, Regular conditional expectations of correspondances, Theor. Prob. Appl. 21 (1976) 325.","journal-title":"Theor. Prob. Appl."},{"key":"BF02204813_CR13","unstructured":"M. El Bouamri and A. Foug\u00e8res, Int\u00e9grandes normales et esp\u00e9rances conditionnelles; espaces d'Orlicz conditionnelles, Travaux du S\u00e9minaire Analyse Convexe de Montpellier 13 (1982)."},{"key":"BF02204813_CR14","first-page":"515","volume":"31","author":"I.V. Evstigneev","year":"1985","unstructured":"I.V. Evstigneev, Regular conditional expectations of random variables depending on parameters, Siam J. Control 31 (1985) 515.","journal-title":"Siam J. Control"},{"key":"BF02204813_CR15","unstructured":"A. Foug\u00e8res, Coercivit\u00e9 des int\u00e9grandes convexes normales, applications \u00e0 la minimisation des fonctionnelles int\u00e9grales et au calcul des variations, Travaux du S\u00e9minaire Analyse Convexe de Montpellier 19 (1976)."},{"key":"BF02204813_CR16","unstructured":"A. Foug\u00e8res, Une extension du th\u00e9or\u00e8me d'inf-\u00e9quicontinuit\u00e9 de J.J. Moreau: Coercivit\u00e9, Convexit\u00e9, Relaxation, Travaux du S\u00e9minaire Analyse Convexe de Montpellier 11 (1977)."},{"key":"BF02204813_CR17","volume-title":"Separability of integrands, working paper","author":"A. Foug\u00e8res","year":"1985","unstructured":"A. Foug\u00e8res, Separability of integrands, working paper, AVAMAC, University of Perpignan, France (1985)."},{"key":"BF02204813_CR18","unstructured":"A. Foug\u00e8res, book in preparation."},{"key":"BF02204813_CR19","volume-title":"\u0394-integrand and essential infimum, Nemickii representation of L.S.C. operators on decomposable spaces and Radon-Nikodym-Hiai representation of measure functionals","author":"A. Foug\u00e8res","year":"1984","unstructured":"A. Foug\u00e8res and A. Truffert, \u0394-integrand and essential infimum, Nemickii representation of L.S.C. operators on decomposable spaces and Radon-Nikodym-Hiai representation of measure functionals, Working paper, AVAMAC, University of Perpignan, France (1984)."},{"key":"BF02204813_CR20","volume-title":"Nonlinear measure functionals, essential regularity and integrals","author":"A. Foug\u00e8res","year":"1986","unstructured":"A. Foug\u00e8res and A. Truffert, Nonlinear measure functionals, essential regularity and integrals, working paper, AVAMAC, University of Perpignan, France (1986)."},{"key":"BF02204813_CR21","volume-title":"Valeurs moyennes conditionnelles","author":"A. Foug\u00e8res","year":"1987","unstructured":"A. Foug\u00e8res and A. Truffert, Valeurs moyennes conditionnelles, Working paper, AVAMAC, University of Perpignan, France (1987)."},{"key":"BF02204813_CR22","volume-title":"Integral representation of additive operators on Lebesgue spaces","author":"F. Hiai","year":"1977","unstructured":"F. Hiai, Integral representation of additive operators on Lebesgue spaces, Working paper, Department of Mathematics, University of Tokyo, Japan (1977)."},{"key":"BF02204813_CR23","doi-asserted-by":"crossref","first-page":"300","DOI":"10.2996\/kmj\/1138036062","volume":"2","author":"F. Hiai","year":"1979","unstructured":"F. Hiai, Representation of additive functionals on vector valued normed KOTHE spaces, Koda\u00ef Math. J. 2 (1979) 300.","journal-title":"Koda\u00ef Math. J."},{"key":"BF02204813_CR24","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0047-259X(77)90037-9","volume":"7","author":"F. Hiai","year":"1977","unstructured":"F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multivalued functions, J. Multivariate Anal. 7 (1977) 149.","journal-title":"J. Multivariate Anal."},{"key":"BF02204813_CR25","unstructured":"J.B. Hiriart Urruty, Th\u00e8se d'\u00e9tat IV, Clermont-Ferrand (1977)."},{"key":"BF02204813_CR26","doi-asserted-by":"crossref","first-page":"123","DOI":"10.7146\/math.scand.a-11878","volume":"47","author":"J.B. Hiriart Urruty","year":"1980","unstructured":"J.B. Hiriart Urruty, Lipschitzr-continuity of the approximate subdifferential of a convex function, Math. Scand. 47 (1980) 123.","journal-title":"Math. Scand."},{"key":"BF02204813_CR27","first-page":"1","volume":"26","author":"A.D. Ioffe","year":"1972","unstructured":"A.D. Ioffe and V.L. Levin, Subdifferentials of convex functions, Trans. Moscow Math. Soc. 26 (1972) 1.","journal-title":"Trans. Moscow Math. Soc."},{"key":"BF02204813_CR28","unstructured":"H.A. Klei, Repr\u00e9sentation int\u00e9grale de fonctions additives, Th\u00e8se 3\u00e8me cycle, Paris (1979)."},{"key":"BF02204813_CR29","first-page":"643","volume":"297","author":"H.A. Klei","year":"1983","unstructured":"H.A. Klei, Le Theor\u00e8me de Radon-Nikodyn pour des multi-mesures \u00e0 valeurs faiblement compactes, C. R. Acad. Sci. Paris 297 (1983) 643.","journal-title":"C. R. Acad. Sci. Paris"},{"key":"BF02204813_CR30","first-page":"303","volume":"307","author":"H.A. Klei","year":"1988","unstructured":"H.A. Klei, Sur la d\u00e9sint\u00e9gration de fonctionnelles inf-compactes, C. R. Acad. Sci. Paris 307 (1988) 303.","journal-title":"C. R. Acad. Sci. Paris"},{"key":"BF02204813_CR31","doi-asserted-by":"crossref","unstructured":"A. Kozek and Z. Suchanecki, Multifunctions of faces for conditional expectations of selections and Jensen's inequality, J. Multivariate Anal. 10 (198) 579.","DOI":"10.1016\/0047-259X(80)90071-8"},{"key":"BF02204813_CR32","unstructured":"P.J. Laurent,Approximation et Optimisation (Hermann, 1972)."},{"key":"BF02204813_CR33","unstructured":"J. Neveu,Bases Math\u00e9matiques du Calcul des Probabilit\u00e9s (Masson, 1970)."},{"key":"BF02204813_CR34","unstructured":"J. Neveu,Martingales \u00e0 temps discret (Masson, 1972)."},{"key":"BF02204813_CR35","volume-title":"Stochastic nonsmooth analysis I: convex integrands","author":"N. Papageorgiou","year":"1986","unstructured":"N. Papageorgiou, Stochastic nonsmooth analysis I: convex integrands, Working paper, University of California, Davis (1986)."},{"key":"BF02204813_CR36","volume-title":"Stochastic nonsmooth analysis II: non-convex integrands and conical approximations of random sets","author":"N. Papageorgiou","year":"1986","unstructured":"N. Papageorgiou, Stochastic nonsmooth analysis II: non-convex integrands and conical approximations of random sets, Working paper, University of California, Davis, (1986)."},{"key":"BF02204813_CR37","doi-asserted-by":"crossref","first-page":"525","DOI":"10.2140\/pjm.1968.24.525","volume":"24","author":"R.T. Rockafellar","year":"1968","unstructured":"R.T. Rockafellar, Integrals which are convex functionals (I), Pac. J. Math. 24 (1968) 525.","journal-title":"Pac. J. Math."},{"key":"BF02204813_CR38","doi-asserted-by":"crossref","first-page":"439","DOI":"10.2140\/pjm.1971.39.439","volume":"39","author":"R.T. Rockafellar","year":"1971","unstructured":"R.T. Rockafellar, Integrals which are convex functionals (II), Pac. J. Math. 39 (1971) 439.","journal-title":"Pac. J. Math."},{"key":"BF02204813_CR39","doi-asserted-by":"crossref","unstructured":"R.T. Rockafellar, Integral functionals, normal integrands and measurable multifunctions, in:Nonlinear Operators and the Calculus of Variations, ed. L. Waelbroeck, Lecture Notes in Mathematics 543 (Springer, 1976) p. 157.","DOI":"10.1007\/BFb0079944"},{"key":"BF02204813_CR40","doi-asserted-by":"crossref","unstructured":"R.T. Rockafellar and R. Wets, Non-anticipativity andL 1-martingales in stochastic optimization problems, Math. Progr. Studies 6 (1976); also in:Stochastic Systems, Modeling, Identification and Optimization, ed. R. Wets (North-Holland, New York, 1976).","DOI":"10.1007\/BFb0120750"},{"key":"BF02204813_CR41","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1080\/17442508208833217","volume":"7","author":"R.T. Rockafellar","year":"1982","unstructured":"R.T. Rockafellar and R. Wets, On the interchange of subdifferentiation and conditional expectation for convex functionals. Stochastics 7 (1982) 173.","journal-title":"Stochastics"},{"key":"BF02204813_CR42","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1080\/17442508308833276","volume":"10","author":"R.T. Rockafellar","year":"1983","unstructured":"R.T. Rockafellar and R. Wets, Deterministic and stochastic optimization problems of Bolza type in discrete time. Stochastics 10 (1983) 273.","journal-title":"Stochastics"},{"issue":"4","key":"BF02204813_CR43","first-page":"337","volume":"XVII","author":"L. Thibault","year":"1981","unstructured":"L. Thibault, Esp\u00e9rances conditionelles d'int\u00e9grandes semi-continus, Calcul des probabilit\u00e9s et statistiques XVII, 4 (1981) 337.","journal-title":"Calcul des probabilit\u00e9s et statistiques"},{"key":"BF02204813_CR44","unstructured":"A. Truffert, Int\u00e9grandes normaux et esp\u00e9rance conditionnelle (II) existence, unicit\u00e9, r\u00e9gularit\u00e9. Travaux du S\u00e9minaire Analyse Convexe de Montpellier 8 (1983)."},{"key":"BF02204813_CR45","volume-title":"Sur la permutation des op\u00e9rateurs esp\u00e9rance conditionnelle et sous-diff\u00e9rentiel","author":"A. Truffert","year":"1985","unstructured":"A. Truffert, Sur la permutation des op\u00e9rateurs esp\u00e9rance conditionnelle et sous-diff\u00e9rentiel, Working paper, AVAMAC, University of Perpignan. France (1985)."},{"key":"BF02204813_CR46","first-page":"265","volume":"50","author":"M. Valadier","year":"1971","unstructured":"M. Valadier, Multiapplications mesurables \u00e0 valeurs convexes compactes, J. Math. Pures et Appl. 50 (1971) 265.","journal-title":"J. Math. Pures et Appl."},{"key":"BF02204813_CR47","unstructured":"M. Valadier, Sur l'esp\u00e9rance conditionnelle multivoque. Travaux du S\u00e9minaire Analyse Convexe de Montpellier 9 (1978)."},{"issue":"126","key":"BF02204813_CR48","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01762501","volume":"4","author":"M. Valadier","year":"1980","unstructured":"M. Valadier, On conditional expectation of random sets, Ann. di Mat. Pura ed Appl. 4, 126 (1980) 81.","journal-title":"Ann. di Mat. Pura ed Appl."},{"key":"BF02204813_CR49","unstructured":"M. Valadier, Sur l'esp\u00e9rance conditionnelle multivoque non convexe, Ann. Inst. H. Poincar\u00e9, Sec. B 16 (1980)."},{"key":"BF02204813_CR50","first-page":"365","volume":"8","author":"B. Cutsem Van","year":"1972","unstructured":"B. Van Cutsem, Martingales de convexes ferm\u00e9s al\u00e9atoires en dimension finie, Ann. Inst. H. Poincar\u00e9, Sect. B 8 (1972) 365.","journal-title":"Ann. Inst. H. Poincar\u00e9, Sect. B"},{"key":"BF02204813_CR51","unstructured":"B. Van Cutsem, Esp\u00e9rance conditionnelles d'une multiapplication \u00e0 valeurs convexes compactes, C. R. Acad. Sci. Paris, Ser. A (1969) 212."},{"key":"BF02204813_CR52","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1137\/0315056","volume":"15","author":"D.H. Wagner","year":"1977","unstructured":"D.H. Wagner, Survey of measurable selection theorems, Siam J. Control 15 (1977) 859.","journal-title":"Siam J. Control"},{"key":"BF02204813_CR53","doi-asserted-by":"crossref","unstructured":"R. Wets, On inf-compact mathematical programms, in:Proc. 5th I.F.I.P. Conf. on Optimization Techniques, Part. I, Lecture Notes in Computer Science 5 (Springer, 1974) p. 426.","DOI":"10.1007\/3-540-06583-0_42"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02204813.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02204813\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02204813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T02:49:39Z","timestamp":1586486979000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02204813"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,12]]},"references-count":53,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,12]]}},"alternative-id":["BF02204813"],"URL":"https:\/\/doi.org\/10.1007\/bf02204813","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,12]]}}}