Bulletin of the American Mathematical Society

MathSciNet review: 1567090
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Book Information:

Authors: 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.

H. A. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations 19 (1975), no. 2, 386–398. MR 430368, DOI 10.1016/0022-0396(75)90011-X

Jean-Pierre Aubin, Arrigo Cellina, and John Nohel, Monotone trajectories of multivalued dynamical systems, Ann. Mat. Pura Appl. (4) 115 (1977), 99–117 (1978). MR 494247, DOI 10.1007/BF02414712

Robert J. Aumann, Markets with a continuum of traders, Econometrica 32 (1964), 39–50. MR 172689, DOI 10.2307/1913732

Claude Berge, Espaces topologiques: Fonctions multivoques, Collection Universitaire de Mathématiques, Vol. III, Dunod, Paris, 1959 (French). MR 0105663

H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies, No. 5, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973 (French). MR 0348562

Frank H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247–262. MR 367131, DOI 10.1090/S0002-9947-1975-0367131-6

Frank H. Clarke, A new approach to Lagrange multipliers, Math. Oper. Res. 1 (1976), no. 2, 165–174. MR 414104, DOI 10.1287/moor.1.2.165

Frank H. Clarke, Optimal control and the true Hamiltonian, SIAM Rev. 21 (1979), no. 2, 157–166. MR 524510, DOI 10.1137/1021027

Ivar Ekeland, Topologie différentielle et théorie des jeux, Topology 13 (1974), 375–388 (French). MR 356899, DOI 10.1016/0040-9383(74)90028-7

Ivar Ekeland and Roger Temam, Analyse convexe et problèmes variationnels, Collection Études Mathématiques, Dunod, Paris; Gauthier-Villars, Paris-Brussels-Montreal, Que., 1974 (French). MR 0463993

A. F. Filippov, On some questions in the theory of optimal regulation: existence of a solution of the problem of optimal regulation in the class of bounded measurable functions, Vestnik Moskov. Univ. Ser. Mat. Meh. Astr. Fiz. Him. 1959 (1959), no. 2, 25–32 (Russian). MR 0122650

12.

A. Fillipov, On the existence of solutions of differential equations with multivalued right-hand side, Mat. Zametki 10 (1971), 307-313.

Hubert Halkin and Edward C. Hendricks, Subintegrals of set-valued functions with semianalytic graphs, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 365–372. MR 229782, DOI 10.1073/pnas.59.2.365

Claude 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, DOI 10.1016/0022-247X(73)90192-3

Henry Hermes and Joseph P. LaSalle, Functional analysis and time optimal control, Mathematics in Science and Engineering, Vol. 56, Academic Press, New York-London, 1969. MR 0420366

16.

Hildenbrand and Kirmann, Introduction to equilibrium analysis, North-Holland, 1976.

Aldo J. Lazar, Spaces of affine continuous functions on simplexes, Trans. Amer. Math. Soc. 134 (1968), 503–525. MR 233188, DOI 10.1090/S0002-9947-1968-0233188-2

Joram Lindenstrauss, A short proof of Liapounoff’s convexity theorem, J. Math. Mech. 15 (1966), 971–972. MR 0207941

Ernest Michael, Continuous selections. I, Ann. of Math. (2) 63 (1956), 361–382. MR 77107, DOI 10.2307/1969615

Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4

John von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401–485. MR 29101, DOI 10.2307/1969463

R. Tyrrell Rockafellar, Convex analysis, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Reprint of the 1970 original; Princeton Paperbacks. MR 1451876

23.

R. Starr, Quasi equilibria in markets with nonconvex preferences, Econometrica 37 (1967), 25-36.

Daniel H. Wagner, Survey of measurable selection theorems, SIAM J. Control Optim. 15 (1977), no. 5, 859–903. MR 486391, DOI 10.1137/0315056

R. T. Rockafellar, Measurable dependence of convex sets and functions on parameters, J. Math. Anal. Appl. 28 (1969), 4–25. MR 247019, DOI 10.1016/0022-247X(69)90104-8

1.

H. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations 19 (1975), 386-398. MR 0430368

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