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Some Theorems in Measure Theory and Generalized Dynamical Systems Defined by Contingent Equations

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Mathematical Systems Theory and Economics I / II

Part of the book series: Lecture Notes in Operations Research and Mathematical Economics ((LNE,volume 11/12))

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Abstract

In this section, we establish two theorems related to the theory of relaxed control introduced by Gamkrelidze, Ghouila-Houri, Warga, and others. We first give some notations and definitions.

This work has been achieved under the direction of Prof. Pallu de La Barriere with the support of DGRT (convention de Recherches 63 FR 199)

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References

  1. Bourbaki, N.: Intégration, Livre VI, ch. 4.

    Google Scholar 

  2. Castaing, Ch.: Sur les équations différentielles multivoques, C.R., t. 263, p. 63–66, 1966

    MathSciNet  MATH  Google Scholar 

  3. — Sur les multi-applications mesurables, Faculté des sciences Caen 1966

    Google Scholar 

  4. — Sur un théoreme de représentation intégrale lié a la comparaison des mesures, Faculté des Sciences Caen 1967

    Google Scholar 

  5. Cesari, L.: Existence theorem for optimal solution in Lagrange and Pontrjagin problems, J Siam Control, vol. 3, 1966

    Google Scholar 

  6. Filippov, A.F.: On certain questions in the theory of optimal control, Vesnik Moskov, Ser. Math. 1959

    Google Scholar 

  7. — Differential equations with many valued discontinuous right hand side Doklady Akad. Nauk, SSSR, t. 151, 1963

    Google Scholar 

  8. Gamkrelidze, R.V.: Optimal sliding states, Doklady, t. 143, no. 2

    Google Scholar 

  9. Ghouila-Houri: Problemes d’existence de commandes optimales, Seminaire d’automatique théorique Faculté des Sciences Caen 1965

    Google Scholar 

  10. — Equations différentielles multivoques, C.R. t. 261, 1965, p. 2568-2570

    Google Scholar 

  11. Karlin, S.: Extreme points of vector functions, Proc. Amer. Math. Soc. Vol. 4, p. 603–610, 1953

    Article  MathSciNet  MATH  Google Scholar 

  12. Lasota, A. Opial, Z.: An application of the Kakutani Ky-Fan theorem in the theory of ordinary differential equation, Bul. Ac. Pol. Sc. Math., vol. XIII, no. 11–12, 1965

    Google Scholar 

  13. Plis, A.: Measurable orientor fields, Bul. Acad. Pol. Sc. Math., vol. 13, no. 8, 1965

    Google Scholar 

  14. Ionescu-Tulcea, A. Ionescu-Tulcea, C.: Disintegration of measures, Ann. INST. FOURIER, Grenoble, t. 14, no. 2, 1964, p. 445–472

    Article  MathSciNet  MATH  Google Scholar 

  15. Warga, J.: Relaxed variational problems, Journal of Math. Analysis and Applications, vol. 4, 1962, p. 111–128

    Article  MathSciNet  MATH  Google Scholar 

  16. Wazewski, T.: Sur une généralisation de la notion des solutions d’une équation au contingent, Bull. Acad. Pol. Math. t. 10, p. 11-15

    Google Scholar 

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© 1969 Springer-Verlag Berlin Heidelberg

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Castaing, C. (1969). Some Theorems in Measure Theory and Generalized Dynamical Systems Defined by Contingent Equations. In: Kuhn, H.W., Szegö, G.P. (eds) Mathematical Systems Theory and Economics I / II. Lecture Notes in Operations Research and Mathematical Economics, vol 11/12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46196-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-46196-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04635-6

  • Online ISBN: 978-3-642-46196-5

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