Journal of Optimization Theory and Applications

, Volume 18, Issue 2, pp 285–289 | Cite as

On the uniform convergence of samples of lebesgue integrals

  • G. F. Bryant
Technical Note

Abstract

Developments and generalizations of a theorem of Halkin, on the limit of the multiple balayage of vector integrals, are deduced via Riemann integration theory.

Key Words

Uniform convergence of sampled integrals multiple balayage theorems continuous maximum principle 

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References

  1. 1.
    Halkin, H.,On the Uniform Limit of Multiple Balayage of Vector Integrals, American Mathematics Monthly, Vol. 73, pp. 733–735, 1966.Google Scholar
  2. 2.
    Goodman, G. S.,Uniform Convergence of Samples of Lebesgue Integrals, Journal of Optimization Theory and Applications, Vol. 10, pp. 331–333, 1972.Google Scholar
  3. 3.
    Adams, C. R., andMorse, A. P.,Random Sampling in the Evaluation of a Lebesgue Integral, Bulletin of the American Mathematical Society, Vol. 45, pp. 442–447, 1939.Google Scholar
  4. 4.
    Halkin, H.,Mathematical Foundations of System Optimization, Topics in Optimization, Edited by G. Leitmann, Academic Press, New York, New York, 1967.Google Scholar
  5. 5.
    Bryant, G. F., andMayne, D. Q.,The Maximum Principle, International Journal of Control, Vol. 20, pp. 1021–1054, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • G. F. Bryant
    • 1
  1. 1.Industrial Automation Group, Department of Computing and ControlImperial CollegeLondonEngland

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