Correction and extension of ``Measurable quotients of unipotent translations on homogeneous spaces"

The statements of Main Theorem 1.1 and Theorem 2.1 of the author's paper [Trans. Amer. Math. Soc. 345 (1994), 577-594] should assume that $\Gamma$ is discrete and $G$ is connected. (Corollaries 1.3, 5.6, and 5.8 are affected similarly.) These restrictions can be removed if the conclusions of the results are weakened to allow for the possible existence of transitive, proper subgroups of $G$. In this form, the results can be extended to the setting where $G$ is a product of real and $p$-adic Lie groups.