 Let \(s_i (\omega)\) denote the strategy chosen by agent \(i\) at possible world \(\omega\). Then \(s: \Omega \rightarrow S\) defined by \(s(\omega) = ( s_1 (\omega),\ldots ,s_n (\omega) )\) is a correlated \(n\)-tuple. Given that \(\mathcal{H}_i\) is a partition of  \(\Omega\),[29]  the function \(s_i : \Omega \rightarrow s_i\) defined by \(s\) is \(\mathcal{H}_i\)-measurable if for each \(\mathcal{H}_{ij} \in \mathcal{H}_{i}, s_i (\omega')\) is constant for each \(\omega' \in \mathcal{H}_{ij}.\) \(\mathcal{H}_i\)-measurability is a formal way of saying that \(i\) knows what she will do at each possible world, given her information.