Density of states

Repetit

Can someone explain to me why the density of states in 2D and 1D includes a step function? I have calculated the DOS in 2D to be:

[tex]
D_2(E) = \frac{m_e}{\pi \hbar^2}
[/tex]

but in my book there a sum over step functions included so that the expression is:

[tex]
D_2(E) = \frac{m_e}{\pi \hbar^2} \sum_m \theta(E - E_m).
[/tex]

What does that step function do? It has something to do with the fact that there are a number of quantized states too right?

Thanks