On ws-Convergence of Product Measures

References

  • Aldous D. J. Limit theorems for subsequences of arbitrarily-dependent sequences of random variables. Z. Wahrscheinlichkeitsth. Verw. Geb. (1977) 40:59–82CrossrefGoogle Scholar
  • Artstein Z. A note on Fatou's lemma in several dimensions. J. Math. Econom. (1979) 6:277–282CrossrefGoogle Scholar
  • Ash R. B.Real Analysis and Probability (1972) (Academic Press, New York) Google Scholar
  • Balder E. J. On a useful compactification for optimal control problems. J. Math. Anal. Appl. (1979) 72:391–398CrossrefGoogle Scholar
  • Balder E. J. A unifying note on Fatou's lemma in several dimensions. Math. Oper. Res. (1984a) 9:267–275LinkGoogle Scholar
  • Balder E. J. A general approach to lower semicontinuity and lower closure in optimal control theory. SIAM J. Control Optim. (1984b) 22:570–598CrossrefGoogle Scholar
  • Balder E. J. Existence results without convexity conditions for general problems of optimal control with singular components. J. Math. Anal. Appl. (1984c) 101:527–539CrossrefGoogle Scholar
  • Balder E. J. An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems. Rend. Circ. Mat. Palermo (1985) 34(II):427–447CrossrefGoogle Scholar
  • Balder E. J. Generalized equilibrium results for games with incomplete information. Math. Oper. Res. (1988) 13:265–276LinkGoogle Scholar
  • Balder E. J. On Prohorov's theorem for transition probabilities. Sém. Anal. Convexe (1989a) 19:9.1–9.11Google Scholar
  • Balder E. J. On compactness of the space of policies in stochastic dynamic programming. Stochastic Processes Appl. (1989b) 32:141–150CrossrefGoogle Scholar
  • Balder E. J., Edgar G. A., Sucheston L. Unusual applications of a.e. convergence. Almost Everywhere Convergence (1989c) (Academic Press, New York) 31–53Google Scholar
  • Balder E. J. New sequential compactness results for spaces of scalarly integrable functions. J. Math. Anal. Appl. (1990) 151:1–16CrossrefGoogle Scholar
  • Balder E. J. On equivalence of strong and weak convergence in L1-spaces under extreme point conditions. Israel J. Math. (1991) 75:21–47CrossrefGoogle Scholar
  • Balder E. J. Existence without explicit compactness in stochastic dynamic programming. Math. Oper. Res. (1992) 17:572–580LinkGoogle Scholar
  • Balder E. J. Lectures on Young Measures. Cahiers du Centre de Recherche de Mathématiques de la Décision (CEREMADE) (1995) 9517(Université Paris-Dauphine, Paris, France) Google Scholar
  • Balder E. J., Ioffe A., Reich S., Shafrir I. New fundamentals of Young measure theory. Calculus of Variations and Optimal Control (2000a) 411(CRC Press, Boca Raton, FL) 24–48Chapman and Hall/CRC Research Notes in MathematicsGoogle Scholar
  • Balder E. J. Lectures on Young measure theory and its applications in economics (Proceedings Grado School on Measure Theory and Real Analysis). Rend. Sem. Matem. Trieste (2000b) 31:1–69Google Scholar
  • Balder E. J., Hess C. Two generalizations of Komlós' theorem with lower closure-type applications. J. Convex Anal. (1996) 3:25–44Google Scholar
  • Balder E. J., Pistorius M. On an optimal consumption problem for p-integrable consumption plans. Econ. Theory (2001) 17:721–737CrossrefGoogle Scholar
  • Balder E. J., Yannelis N. C. Upper semicontinuity of the Cournot-Nash equilibrium correspondence: A general approach. (2000) . ForthcomingGoogle Scholar
  • Berliocchi H., Lasry J. M. Intégrandes normales et mesures paramétrées en calcul des variations. Bull. Soc. Math. France (1973) 101:129–184CrossrefGoogle Scholar
  • Bertsekas D. P., Shreve S. E.Stochastic Optimal Control: the Discrete Time Case (1978) (Academic Press, New York) Google Scholar
  • Billingsley P.Convergence of Probability Measures (1968) (Wiley, New York) Google Scholar
  • Billingsley P.Probability and Measure (1986) (Wiley, New York) Google Scholar
  • Bourbaki N.Topologie Générale (1974) (Hermann, Paris, France) Google Scholar
  • Brooks J., Chacon R. V. Continuity and compactness of measures. Adv. Math. (1980) 37:16–26CrossrefGoogle Scholar
  • Castaing C., Valadier M.Convex Analysis and Measurable Multifunctions (1977) 580(Springer-Verlag, Berlin, Germany) Lecture Notes in MathematicsCrossrefGoogle Scholar
  • Chatterji S. D., Bretagnolle J. L., et al. Les martingales et leurs applications analytiques. Ecole d'Été de Probabilités: Processus Stochastiques (1973) 307(Springer-Verlag, Berlin, Germany) 27–164Lecture Notes in MathematicsCrossrefGoogle Scholar
  • Chatterji S. D. A subsequence principle theory. Jber. d. Dt. Math.-Verein (1985) 87:91–107Google Scholar
  • Choquet G.Lectures on Analysis (1969) (Benjamin, Reading, MA) Google Scholar
  • Dal Maso G.An Introduction to Γ-Convergence (1993) (Birkhäuser, Boston, MA) CrossrefGoogle Scholar
  • Dellacherie C., Meyer P.-A.Probabilités et Potentiel (1975) (Hermann, Paris, France) . (English translation: North-Holland, Amsterdam, The Netherlands)Google Scholar
  • Galdéano F. Convergence étroite de mesures définies sur un espace produit Thèse de doctorat. (1997) (Université de Perpignan, Académie de Montpellier, Perpignan, France) Google Scholar
  • Galdéano F., Truffert A. On the narrow convergence of measures defined on a product space. (1998) . PreprintGoogle Scholar
  • Gänssler P. Compactness and sequential compactness inspaces of measures. Z. Wahrscheinlichkeitsth. Verw. Geb. (1971) 17:124–146CrossrefGoogle Scholar
  • Gaposhkin V. F. Convergence and limit theorems for sequences of random variables. Theory Probab. Appl. (1972) 17(3):379–400CrossrefGoogle Scholar
  • Greenberg J., Shitovitz B., Wieczorek A. Existence of equilibria in atomless production economies with price dependent preferences. J. Math. Econom. (1979) 6:31–41CrossrefGoogle Scholar
  • Jacod J., Mémin J., Azéma J., Yor M. Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité. Séminaire de Probabilités XV (1981) 850(Springer-Verlag, Berlin, Germany) 529–546Lecture Notes in MathematicsCrossrefGoogle Scholar
  • Jacod J., Mémin J., Azéma J., Yor M. Rectification à: Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité. Séminaire de Probabilités XVII (1983) 986(Springer-Verlag, Berlin, Germany) 509–511Lecture Notes in MathematicsCrossrefGoogle Scholar
  • Jawhar A. Mesures de transition et applications. Sém. Analyse Convexe Montpellier (1984) 14:13.1–13.62Google Scholar
  • Komlós J. A generalisation of a problem of Steinhaus. Acta Math. Acad. Sci. Hungar. (1967) 18:217–229CrossrefGoogle Scholar
  • LeCam L. M. Convergence in distribution of stochastic processes. Univ. California Publ. Statist. (1957) 2(11):207–236Google Scholar
  • Mas-Colell A. On a theorem of Schmeidler. J. Math. Econom. (1984) 13:201–206CrossrefGoogle Scholar
  • Neveu J.Mathematical Foundations of the Calculus of Probability (1965) (Holden-Day, San Francisco, CA) Google Scholar
  • Nowak A. On the weak topology on a space of probability measures induced by policies. Bull. Polish Acad. Sci. Math. (1988) 36:181–186Google Scholar
  • Pedregal P.Parametrized Measures and Variational Principles (1997) (Birkhäuser, Basel, Switzerland) CrossrefGoogle Scholar
  • Prohorov Yu. V. Convergence of random processes and limit theorems in probability theory. Theory Probab. Appl. (1956) 1:157–214CrossrefGoogle Scholar
  • Schäl M. On dynamic programming: compactness of the space of policies. Stochastic Processes Appl. (1975) 3:345–364CrossrefGoogle Scholar
  • Schmeidler D. Fatou's lemma in several dimensions. Proc. Amer. Math. Soc.24:300–306Google Scholar
  • Schmeidler D. Equilibirum points of non-atomic games. Proc. Amer. Math. Soc. (1973) 24:300–306Google Scholar
  • Schwartz L.Radon Measures (1975) (Oxford University Press, Oxford, U.K.) Google Scholar
  • Stout W. F.Almost Sure Convergence (1974) (Academic Press, New York) Google Scholar
  • Valadier M. Désintégration d'une mesure sur un produit. C. R. Acad. Sci. Paris (1973) 276:33–35Google Scholar
  • Valadier M., Cellina A. Young measures. Methods of Nonconvex Analysis (1990) 1446(Springer-Verlag, Berlin, Germany) 152–188Lecture Notes in MathCrossrefGoogle Scholar
  • Valadier M. La loi forte des grands nombres comme conséquence d'autres théorèmes. Sém. Analyse Convexe Montpellier (1991) 21:15.1–15.6Google Scholar
  • Warga J.Optimal Control of Differential and Functional Equations (1972) (Academic Press, New York) Google Scholar
  • Yushkevich A. The compactness of a policy space in dynamic programming via an extension theorem for Carathéodory functions. Math. Oper. Res. (1997) 22:458–467LinkGoogle Scholar
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