or every $t \geq 0$ we have $$\int_{\mathcal{N}(S \times G)} S_t^{\Lambda|\eta}(f)(\sigma) d\mu(\sigma) = \int_{\mathcal{N}(S \times G)} f(\sigma) d\mu(\sigma)$$ for every bounded $\mathcal{F}_{\Lambda \times G}$-measurable function $f: \mathcal{N}(S \times G) \to {{\mathbb R}}$.  0.  We say that $\mu$ is *reversible* for the 