Characterizations of the subdifferential of convex integral functions under qualification conditions

This work provides formulae for the $\epsilon$-subdifferential of integral functions in the framework of complete $\sigma$-finite measure spaces and locally convex spaces. In this work we present here new formulae for this $\epsilon$-subdifferential under the presence of continuity-type qualification conditions relying on the data involved in the integrand. the integral function $I_f$ are also presented.