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

Volume of the moduli space of unmarked bounded positive convex $\mathbb{RP}^2$ structures