Geodesic
Introduction to the theory of noncommutative integration
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 27 (1985), pp. 167-190.

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We present a survey of the contemporary state of the theory of integration in von Neumann and $JBW$ algebras. 
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     title = {Introduction to the theory of noncommutative integration},
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N. V. Trunov; A. N. Sherstnev. Introduction to the theory of noncommutative integration. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 27 (1985), pp. 167-190. http://geodesic.mathdoc.fr/item/INTD_1985_27_a5/