[see also: explain, justify, ground]
This argument is invalid for several reasons.
It is for this reason that his argument is incorrect.
The definition is stated in terms of local martingales, rather than martingales, for the technical reason that the former are easier to characterize in applications.
This is the reason for calling $f$ the derivative of $g$.
One reason for using this rather elaborate model is that it permits a simple and concrete definition of the realization.
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.
The reason that this is significant is that ......
Indeed, there is reason to suspect that difficulties could increase with increasing $n$.
There is no reason to expect this to be an inverse map on $K$, but we do have the following.
To see this, we reason as follows.
The simplest way is to reason by induction on $n$.
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