  For the moduli space of unmarked convex $\mathbb{RP}^2$ structures on the
surface $S_{g,m}$ with negative Euler characteristic, we investigate the
subsets of the moduli space defined by the notions like boundedness of
projective invariants, area, Gromov hyperbolicity constant, quasisymmetricity
constant etc. These subsets are comparable to each other. We show that the
Goldman symplectic volume of the subset with certain projective invariants
bounded above by $t$ and fixed boundary simple root lengths $\mathbf{L}$ is
bounded above by a positive polynomial of $(t,\mathbf{L})$ and thus the volume
of all the other subsets are finite. We show that the analog of Mumford's
compactness theorem holds for the area bounded subset.
