  In this paper we prove two multiset analogs of classical results. We prove a
multiset analog of Lovasz's version of the Kruskal-Katona Theorem and an analog
of the Bollobas-Thomason threshold result. As a corollary we obtain the
existence of pebbling thresholds for arbitrary graph sequences. In addition, we
improve both the lower and upper bounds for the `random pebbling' threshold of
the sequence of paths.
