statistical mechanics - The definition of Density of States

The density of states (DOS) is generally defined as

$$D(E)=\frac{d\Omega(E)}{dE},$$ where $\Omega(E)$ is the number of states in a volume $V$. But why DOS can also be defined using delta function, as $$D(E)~=~\sum\limits_{n} \int \frac{d^3k}{(2\pi)^3}\delta(E-\epsilon_n(\mathbf{k}))?$$