The sheaf conjecture for continuous valuations

Let $X$ be a manifold, and for each open subset $U\subset X$ let ${\cal S}_i(U)$ be the space of continuous valuations on $U$. These spaces form a presheaf ${\cal S}_{i,X}$ on $X$. Sheaf conjecture for continuous valuations. The presheaf ${\cal S}_{i,X}$ is a sheaf. This conjecture asserts that continuous valuations satisfy the sheaf gluing and locality properties; its resolution is not specified in the source.