Summary
If M[ℬ, U(C, C)] is the collection of U(C, C)-valued (non-linear) set functions defined on the Borel subsetsℬ of the compact Hausdorff space S, one may define operators on M[ℬ, U(C, C)] which are « of the Hammerstein type ». We initiate a study of a concept analogous to the second dual of a space of continuous functions by inquiring as to what representation theorems one may obtain for these operators. A « Lebesgue type » decomposition theorem for elements of M[ℬ, U(C, C)] is obtained. A « density » theorem is also obtained for the space M[ℬ, U(C, C)].
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Entrata in Redazione il 6 marzo 1974.
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Alò, R.A., Cheney, C.A. & de Korvin, A. Non-linear operators on sets of measures. Annali di Matematica 109, 1–22 (1976). https://doi.org/10.1007/BF02416951
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DOI: https://doi.org/10.1007/BF02416951