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Given a von Neumann algebra M we consider the central extension E(M) of M. We describe class of von Neumann algebras M for which the algebra E(M) coincides with the algebra S(M)—the algebra of all measurable operators with respect to M, and with S(M, τ)—the algebra of all τ-measurable operators with respect to M.

Conditions of coincidence of central extensions of von Neumann algebras and algebras of measurable operators