Abstract
In the present paper, we prove a selector theorem in Banach spaces similar to that of Filippov (Ref. 1), but where the measurability of the selected function follows from a weak upper semicontinuity property.
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References
Filippov, A. F.,On Certain Questions in the Theory of Optimal Control, SIAM Journal on Control, Vol. 1, No. 1, 1962.
Cesari, L.,Existence Theorems for Multidimensional Lagrange Problems, Journal of Optimization Theory and Applications, Vol. 1, No. 2, 1967.
McShane, E. J., andWarfield, R. B.,On Filippov's Implicit Functions Lemma, Proceedings of the American Mathematical Society, Vol. 18, No. 1, 1967.
Hille, E., andPhillips, R. S.,Functional Analysis and Semi-Groups, American Mathematical Society, Providence, Rhode Island, 1957.
Royden, H.,Real Analysis, The Macmillan Company, New York, 1968.
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Communicated by L. Cesari
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Cole, J.K. A selector theorem in Banach spaces. J Optim Theory Appl 7, 170–172 (1971). https://doi.org/10.1007/BF00932474
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DOI: https://doi.org/10.1007/BF00932474