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MR2241426 (2007i:60007) 60B99 (42B35 46A55 46N30)
Safarov, Yu. Birkhoff's theorem for families of probability spaces. (Russian) Algebra i Analiz 17 (2005), no. 5, 141--163; translation in St. Petersburg Math. J. 17 (2006), no. 5, 797–813
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