  Let $\mathcal{H}$ 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 $L^2(\mathcal{H}, \mu)$, where $\mu$
is Lebesgue measure on $\mathcal{H}$, 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.
