Some weak laws of large numbers in noncommutative probability (Q1380107)

Various forms of weak laws of large numbers are presented for noncommutative \(L_p({\mathcal M})\)-spaces, \(p= 1,2,0\) associated with a finite von Neumann algebra \({\mathcal M}\) (here \(L_0({\mathcal M})\) is the space of all measurable operators affiliated with \({\mathcal M})\). At the end of the article, the authors consider also the central limit theorem for freely independent random variables.