Why does integrating the Gibbs ensemble density give infinity?

[emob2p]

Hi,
I'm taking a course in Stat Mach using Kerson and Huang's Statistical Mechanics book. I am quite confused with their treatment of a Gibbsian Ensemble. They say imagine an infinite copies of the same system whose state can be represented by a point in phase space. Then $$\rho (p,q,t) = d^{3N}p d^{3N}q$$ is the number of representative points contained in the infinitesimal volume. So if we integrate this over allowed p's and q's, we should get infinity because we started out w/ an infinite number of total systems. Can this be correct?

 

[actionintegral]

Not if the volume of integration is finite or infinite but integrable.