The MathResource
Moore-Osgood theorem,
n. a theorem guaranteeing that the order of taking iterated limits may be changed. For example, suppose f : X × Y → Z is a mapping between pseudo-metric spaces; if
Maple Image UNIFORMLY for Maple Image
Maple Image POINTWISE for Maple Image
then
Maple Image.
The most common application has Y as the extended natural numbers with b as ∞.