Monotone Property Thresholds

This paper was originally written by the authors circa 2005 but was never submitted for publication. The present version corrects minor errors, adds references to work published since the original draft, and includes a section discussing further research directions. The core framework – the property function ${\psi }_G$, the density function ${\phi }_{\mu }^{\psi }$, and all threshold results – is unchanged from the original.