Geodesic
On the duality of functors generated by spaces of vector-valued functions
Izvestiya. Mathematics , Tome 9 (1975) no. 6, pp. 1213-1240.

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A complete solution is given for the problem of describing the functor dual to a functor generated by a space of measurable vector-valued functions, and also for the problem of describing the rings of operators in these functors. Bibliography: 24 titles. 
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A. V. Bukhvalov. On the duality of functors generated by spaces of vector-valued functions. Izvestiya. Mathematics , Tome 9 (1975) no. 6, pp. 1213-1240. http://geodesic.mathdoc.fr/item/IM2_1975_9_6_a4/

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