Repeated application of (4) shows that......
As an example of the application of Theorem 5, suppose......
Even in the case n=2, the application of Theorem 6 gives essentially nothing better than the inequality......
Specifically, one might hope that a clever application of something like Choquet's theorem would yield the desired conclusion.
As an application, consider the Dirichlet problem Lf=0.
We then show how this leads to stronger results in applications.
[Do not use “application'' when you mean “map'': a map f:X→ Y ( not: “an application f'').]