For a Dirichlet process, there are two parameter $\alpha$ and $H$, and the Dirichlet process $X$ is defined as
$$(X(B\_1),\cdots,X(B\_n))\sim Dir(\alpha H(B\_1),\cdots,\alpha H(B\_n))$$
where$\{B\_i\}\_{i=1}^n$is a partition of the measurable space.


While the Dirichlet distribution is like that
$$f(x\_1,x\_2, \cdots ,x\_{K - 1};\alpha \_1,\alpha \_2, \cdots ,\alpha \_{K - 1},\alpha \_K) = \frac{1}{B(\vec \alpha )}\prod\limits\_{i = 1}^K x\_i^{\alpha\_i - 1} $$


My question is:


If I want to view the Dirichlet distribution as a special case of the Dirichlet process, then how should I set the parameters $\alpha$ and $H$ in the definition of Dirichlet process?



How to extend Dirichlet distribution to Dirichlet process
Here $\alpha$ is a number, and $H$ is a measure.


I believe that you should take a finite space, say, $\{1,...,K\}$. Then for any partition of $\{1,...,K\}$, 
your first formula will hold. $H$ measures the asymmetry of your Dirichlet process, as the parameters $\alpha\_1,...,\alpha\_K$ do in the second formula.


