The predual space of a $\mathrm{JBW}^*$-triple

In the paper $\mathrm{JB}^*$-triples which are dual Banach spaces are considered as analogues of $\mathrm{JBW}^*$-algebras. For $\mathrm{JBW}^*$-triples an analogue of the classical theorem of Vitali–Hahn–Saks on convergent sequences of measures and a theorem on weak compactness of a set of normal functionals are proved.