Let M be a right R-module, (S,

) a strictly totally ordered monoid which is also artinian and

a monoid homomorphism, and let

denote the generalized inverse polynomial module over the skew generalized power series ring [[

]]. In this paper, we prove that

has the same uniform dimension as its coefficient module

, and that if, in addition, R is a right perfect ring and S is a chain monoid, then

has the same couniform dimension as its coefficient module

.