**A. Y. Lo, V. V. Sazonov**

## On Normal Approximation of Large Products of Functions: a Refinement of Blackwell's Result

**abstract:**

An asymptotic expansion for the approximation of standardized
products of large numbers of smooth positive functions by $\exp (-
x^2/2)$ is given. This result is closely related to the Bernstein--von
Mises theorem on the normal approximation of posterior distributions.