DOI: 10.68381/jca02010 ISSN: 0944-6532
On the Measurability of the Conjugate and the Subdifferential of a Normal Integrand
Christian Hess
Let
(T,\mathcal{T})
(
T
,
T
)
be an arbitrary measurable space, X a Banach space whose dual
X^*
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^*
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].