“…[6, Theorem 5]). Suppose U is continuously differentiable, λ refr is continuous, and for λ ± (x) = (±U (x) ∨ 0) + λ refr (x), we have thatlim inf x→∞ λ + (x) > lim sup x→∞ λ − (x) and lim inf x→−∞ λ − (x) > lim sup x→∞ λ + (x).Then there are constants c > 0, α > 0 and a continuous norm-like functionV ∈ L 2 (µ), V > 0 on E, such that for all (x, θ) ∈ E, |P (t)f (x, θ) − π(f )| ≤ c(1 + V (x, θ))e −αt , t ≥ 0,for all measurable f : E → R satisfying |f (x, θ)| ≤ 1 + V (x, θ) on E.…”