Partitions of Unity in Sobolev Spaces over Infinite Dimensional State Spaces

We prove some general results on the existence of partitions of unity consisting of continuous functions in certain Sobolev type spaces on various infinite dimensional manifolds. As special cases we obtain in particular, partitions of unity (a) in the Malliavin test functions on an abstract Wiener space; (b) in the first order Sobolev spaces on pinned and free loop spaces; (c) in the first order Sobolev spaces associated with reversible Fleming–Viot processes.