Relation between the density function (measure theory) and density (physics) I was reading some notes on Ergodic Theory and there is this sentence:

Suppose we distribute mass on $X$ according to the mass density
  $fd\mu$, $f \in L^1(\mu)$,$ f \geq 0$, and then apply $T$ to every
  point in the space (then $T$ is some dynamical system acting on $X$).  What will be the new mass distribution?

My question is, what is the relation between the density FUNCTION $f$ and the density as we study in a Physics course?  
Thanks in advance :)

The terminology comes from physics. The quantity $f(x)$ can be interpreted as the density at the point $x$.
