On the Measurability of the Conjugate and the Subdifferential of a Normal Integrand

Let $(T,\mathcal{T})$ be an arbitrary measurable space, X a Banach space whose dual $X^*$ is strongly separable and f an integrand defined on T × X. If f is normal in the sense of Rockafellar [18], then the conjugate integrand $f^*$ is normal. Moreover the subdifferential multifunction is Effros (or weakly) measurable. These results extend those of Rockafellar [18] and of Hess [6], and provide an alternate approach to that of Beer [2].