  In the framework of the prepotential description of superspace
two-dimensional $(2,2)$ supergravity, we discuss the construction of invariant
integrals. In addition to the full superspace measure, we derive the measure
for chiral superspace, and obtain the explicit expressions for going from
superspace actions to component actions. We consider both the minimal $U_A(1)$
and the extended $U_V(1) \otimes U_A(1)$ theories.
