Equation 13.13.5293FB8527BF9B

\begin{equation} \begin{aligned} \omega ^ n_{P_\omega \left(\min \{ f_1,f_2\} \right)} = & \mathds {1}_{\left\{ P_\omega \left(\min \{ f_1,f_2\} \right)=f_1\right\} }\, \omega ^ n_{f_1} + \mathds {1}_{\left\{ P_\omega \left(\min \{ f_1,f_2\} \right)=f_2\right\} }\, \omega ^ n_{f_2} \\ & - \mathds {1}_{\left\{ P_\omega (\min \{ f_1,f_2\} )=f_1=f_2\right\} }\, \omega ^ n_{f_ j}\\ \geq & \mathds {1}_{\left\{ P_\omega \left(\min \{ f_1,f_2\} \right)=f_ j\right\} }\, \omega ^ n_{f_ j}. \end{aligned} \end{equation}