Before revision: In the dual L ^{\Phi^* of a \Delta_2-Orlicz space L ^\Phi, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology \tau(L ^{\Phi^*,L^\Phi} ,L_\Phi} ) if and only if on each order interval [-\zeta,\zeta]=\{\xi: -\zeta\leq \xi\leq\zeta\} (\zeta\in L ^{\Phi^* ), it is lower semicontinuous (resp. continuous) for the topology of convergence in probability.
After revision: In the dual L _{\Phi^* of a \Delta_2-Orlicz space L ^\Phi, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology \tau(L ^{\Phi^*,L^\Phi} ,L_\Phi} ) if and only if on each order interval [-\zeta,\zeta]=\{\xi: -\zeta\leq \xi\leq\zeta\} (\zeta\in L ^{\Phi^* ), it is lower semicontinuous (resp. continuous) for the topology of convergence in probability.