In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovász's version of the Kruskal–Katona Theorem and an analog of the Bollobás–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.
