Abstract
On a Borel bar space (E,B,-), the following concepts are introduced in a suitable way: measurable fields of real Hilbert spaces, real measurable fields of vectors, operators and Von Neumann (VN) algebras: ξ (⋅),a (⋅),M (⋅). Then a satisfactory real reduction theory is obtained: a real VN algebraM can be represented as a direct integral\(M = \int_{\left( {E, - } \right)}^ \oplus {M(t)dv(t)} \) where each VN algebraM(t) in this field will be simpler.
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