STRONG LAW OF LARGE NUMBERS FOR STATES AND TRACES OF A W-STAR-ALGEBRA - Batty, C (Springer-Verlag, 1979)
Let Mathematical expression be a W*-algebra with faithful normal state ρ. Several different notions of independence with respect to ρ are introduced for operators in Mathematical expression. A non-commutative extension of the strong law of large numbers is proved. When ρ is a trace, this theorem is extended to cover unbounded operators associated with A. © 1979 Springer-Verlag.