Pacific Journal of Mathematics

Carathéodory convex integrand operators and probability theory.

Nikolaos S. Papageorgiou

Article information

Source
Pacific J. Math., Volume 116, Number 1 (1985), 155-184.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102707254

Mathematical Reviews number (MathSciNet)
MR769829

Zentralblatt MATH identifier
0606.49007

Subjects
Primary: 90C48: Programming in abstract spaces
Secondary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}

Citation

Papageorgiou, Nikolaos S. Carathéodory convex integrand operators and probability theory. Pacific J. Math. 116 (1985), no. 1, 155--184. https://projecteuclid.org/euclid.pjm/1102707254


Export citation

References

  • [1] J. P. Aubin, Mathematical Methods of Game and Economic Theory, Studies in Math and Its Applications,Vol. 7, North Holland, Amsterdam (1977).
  • [2] R. Aumann, Integrals of set valuedfunctions, J. Math. Anal. Appl., 12 (1965), 1-12.
  • [3] J. M. Bismut, Integrales convexes et Probabilites, J. Math. Anal. Appl., 42 (1973), 639-73.
  • [4] C. Castaing-M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math Vol. 580 Springer,Berlin(1976).
  • [5] S. D. Chatterji, Martingale convergence and the Radon-Nikodym theorem in Banach Spaces, Math. Scand., 22 (1968), 21-41.
  • [6] J. Diestel-J. J. Uhl, Jr., Vector Measures, Mathematical Surveys, Vol. 15, Amer. Math. So,Providence, Rhode Island(1977).
  • [7] P. Halmos, A Hubert Space Problem Booh, Van Nostrand-Reinhold, New York (1967).
  • [8] F. Hiai-F. Umegaki,Integrals, conditional expectations, and martingales of multival- uedfunctions, J. Mult. Anal., 7 (1977),149-82.
  • [9] C. Himmelberg, Measurable relations, Fund. Math., LXXXVI (1975),53-72.
  • [10] J. B. Hiriart-Urruty, About properties of the mean functional and continuous inf convolution in stochastic convex analysis, in: Optimization Techniques, Modeling and Optimization in the Service of Man, Ed. J. Cea, Springer, Lecture Notes in Computer Science, Berlin (1976),763-89.
  • [11] N. Neumann, On the Strassen disintegration theorem, Arch. Math., 29 (1977), 413-20.
  • [12] N. S. Papageorgiou, Nonsmooth analysis on partially ordered vector spaces: Part I. Convex Case, Pacific J. Math., 107 (1983), 403-458.
  • [13] N. S. Papageorgiou, Nonsmooth analysis on partially ordered vector spaces: Part II. Nonconvex case, Clarke's theory, Pacific J. Math., 109 (1983), 463-495.
  • [14] N. S. Papageorgiou, Nonsmooth Analysis on Partially Ordered Vector Spaces: Part III.The Subdifferential Theory, Presented at the 11th Symposium on Math Programming, (Bonn-August 1982).
  • [15] J. P. Penot, Calculsous differentiel et optimisation, J. Funct. Anal., 27 (1978), 248-76.
  • [16] A. Peressini, Ordered Topological Vector Spaces, Harper and Row, New York (1967).
  • [17] R. T. Rockafellar, Integrals which are convex functional, Pacific J. Math., 24 (1968), 525-38.
  • [18] R. T. Rockafellar, Integrals which are convex functionals II, Pacific J. Math., 39 (1971), 439-69.
  • [19] R. T. Rockafellar, Convex Integral Functionals and Duality, in Contributions to Nonlinear Analysis, ed. Zarontonelli, p. 215-36, Academic Press, New York (1971).
  • [20] R. T. Rockafellar, Integral Functionals, Normal Integrands and Measurable Selections, in Non- linear Operators and the Calculus of Variations, ed. J. Gossez et al., p. 157-207, Lecture Notes in Math, Vol. 543, Springer, Berlin (1976).
  • [21] R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton (1970).
  • [22] J. Saint-Pierre, Une extension du theoreme de Strassen, CR.A.S. t 279 (1974), 5-8.
  • [23] H. H. Schaefer, Banach Lattices and Positive Operators, Springer, New York (1974).
  • [24] M. Valadier, Sous differentiabilite de functions convexes a valeurs dans un espace vectoriel ordonne, Math. Scand., 30 (1972), 65-74.