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An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite 𝑤*-algebras
Suppose that (s%)if¡, is a family of semifinite w*-algebras and that /¿( is a normal state of sft with /¿¡(1) = 1 for each i el.Let s/=0ls, (s/u /¿¡) and let AK-+Ax denote the natural injection of ^ into si.(The notation is explained in §3 below; si is the (/¿^-incomplete …