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.
A drawback to Pólya trees, and perhaps the main reason why they have not seen much application within the Bayesian nonparametric literature, is that an arbitrary partition tree needs to be specified.
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 $f:X\to Y$ ( not: “an application $f$”).]
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