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Book Information

Author(s): C. Castaing and M. Valadier
Title: Convex analysis and measurable multifunctions
Additional book information: Lecture Notes in Math., no. 580, Springer-Verlag, Berlin, Heidelberg, New York, 1977, vii + 278 pp., $11.00

1.: H. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations 19 (1975), 386-398. MR 430368
2.: J. P. Aubin, A. Cellina and J. Nohel, Monotone trajectories of multivalued dynamical systems, MRC Technical Report (1976), University of Wisconsin, Madison. MR 494247
3.: R. Aumann, Markets with a continuum of traders, Econometrica 32 (1964), 39-50. MR 172689
4.: C. Berge, Espaces topologiques et fonctions multivoques, Dunod, Paris, 1959. MR 105663
5.: H. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, 1973. MR 348562
6.: F. Clarke, Generalized gradients and applications Trans. Amer. Math. Soc. 205 (1975), 247-262. MR 367131
7.: F. Clarke, A new approach to Lagrange multipliers, Math of Operations Research 1 (1976), 165-175. MR 414104
8.: F. Clarke, Optimal control and the true Hamiltonian, SIAM Review (to appear). MR 524510
9.: I. Ekeland, Topologie différentielle et theorie des jeux, Topology 13 (1974), 375-388. MR 356899
10.: I. Ekeland and R. Temam, Convex analysis and variational problems, North-Holland-Elsevier, 1976. MR 463994
11.: A. Fillipov, On certain questions in the theory of optimal control, Vestnik Moskov Univ. Ser. Mat. Mek. Astr. Fiz. Him. 2 (1959), 25-32; English translation, Siam J. Control 1 (1962), 76-84. MR 122650
12.: A. Fillipov, On the existence of solutions of differential equations with multivalued right-hand side, Mat. Zametki 10 (1971), 307-313.
13.: H. Halkin and E. Hendricks, Subintegrals of set-valued functions with semianalytic graphs, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 365-367. MR 229782
14.: C. Henry, An existence theorem for a class of differential equations with multivalued right-hand side, J. Math. Anal. Appl. 41 (1973), 179-186. MR 335906
15.: H. Hermes and J. P. La Salle, Functional analysis and time optimal control, Academic Press, New York, 1969. MR 420366
16.: Hildenbrand and Kirmann, Introduction to equilibrium analysis, North-Holland, 1976.
17.: A. J. Lazar, Spaces of affine continuous functions on simplexes, Trans. Amer. Math. Soc. 134 (1968), 503-525. MR 233188
18.: J. Lindenstrauss, A short proof of Liapounoff's convexity theorem, J. Math. Mech 15 (1966), 971-972. MR 207941
19.: E. Michael, Continuous selections. I, Ann. of Math. 63 (1956), 361-382. MR 77107
20.: E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. MR 42109
21.: J. von Neumann, On rings of operators reduction theory, Ann. of Math. 50 (1949), 401-485. MR 29101
22.: R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, N. J., 1970. MR 1451876
23.: R. Starr, Quasi equilibria in markets with nonconvex preferences, Econometrica 37 (1967), 25-36.
24.: D. Wagner, Survey of measurable selection theorems, Siam J. Control and Optimization 15 (1977), 859-903. MR 486391
25.: R. T. Rockafellar, Measurable dependence of convex sets and functions on parameters, J. Math. Anal. Appl. 28 (1969), 4-25. MR 247019

Review Information:
Journal: Bull. Amer. Math. Soc. 84 (1978), 950-956.
DOI: 10.1090/S0002-9904-1978-14543-1
PII: S 0002-9904(1978)14543-1

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ISSN 1936-881X(e) ISSN 0002-9904(p)

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