  Consideration of some perturbatively calculated gauge-invariant expectation
values of local noncomposite operators in pure Yang-Mills theory indicates that
those expectation values which are not dimension specific, and which are well
defined near $D=4$ dimensions, have some {\it finite} limit as the evaluated
expression is naively extrapolated from $D=4$ to $D=2$. If this finite limit is
a generic feature for such quantities it would not only be quite remarkable but
also of some utility : For example, one may then use it as a convenient
necessary condition when checking gauge invariance. Some examples are discussed
at nonzero temperature.
