Defining an arbitrary region

1. Jan 11, 2010

ExtravagantDreams

For some reason I can't seem to think of a simple solution to defining an arbitrary region. I would like to do this so that I can then apply various operations to certain regions. The value of the region is irrelavent, so long as it is constant, it is it's location that I am interested in.

Is there something equivalent to defining points, $$\delta(\vec{r}-\vec{r_i})$$, which defines an entire region?

Can I simply define some region with, $$\int_Vd^3r'\delta(\vec{r}-\vec{r} ')$$ ?

How would I explicitly define the complimentary region of space such that their union defines all of space?

Would it be better to approach this using some sort of distribution?