Theorem:
Suppose
Proof:
Corollaries
The above result can be stated in a variety of ways.
Corollary (#1):
Under the same conditions as the original theorem, if
Proof: Continuous mapping theorem.
Corollary (#2): Under the same conditions as the first corollary,
Proof:
At this point, note that
holds by Slutsky’s theorem.
Finally, note that Corollary #2 holds for any consistent estimator of
by the same proof.