Geodesic
The direct integral of pairs of dual spaces
Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 339-349

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For a family of pairs of vector spaces which are in duality, given on a measure space, we introduce the concept of the direct integral, which is also a pair of vector spaces in duality; and we investigate its properties. We prove that the von Neumann direct integral of Hilbert spaces is a particular case of the direct integral defined here. Bibliography: 9 titles. 
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     author = {M. A. Naimark},
     title = {The direct integral of pairs of dual spaces},
     journal = {Izvestiya. Mathematics },
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     number = {2},
     year = {1976},
     language = {en},
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M. A. Naimark. The direct integral of pairs of dual spaces. Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 339-349. http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a6/