Let $\mathscr{H}$ denote a connected component of a stratum of translation surfaces. We show that the Siegel-Veech transform of a bounded compactly supported function on $\mathbb{R}^2$ is in $L^2(\mathscr{H}, \mu)$, where $\mu$ is the Lebesgue measure on $\mathscr{H}$, and give applications to bounding error terms for counting problems for saddle connections. We also propose a new invariant associated to $SL(2,\mathbb{R})$-invariant measures on strata satisfying certain integrability conditions.
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