Definition

σ\sigma-field generated by a collection of maps


If for all tTt \in T we have Xt/X_t \in \mathcal{B}/\mathcal{B}' then we define σ(Xt,tT)=tTσ(Xt)\sigma(X_t,\, t \in T) = \bigvee_{t \in T} \sigma(X_t).