The Factorization Criterion
Let $U$ be a statistic based on the random sample $Y_1, Y_2,...Y_n$. Then $U$ is a sufficient statistics for the estimation of a parameter $\theta$ if and only if the likelihood $L(\theta)$ can be factored into two non-negative functions, $$L(\theta)=g(u,\theta)h(y_1,y_2,...,y_n)$$
where $g(u,\theta)$ is a function only of $u$ and $\theta$ and $h(y_1,y_2,...,y_n)$ is not a function of $\theta$.
What is the proof for the factorization criterion?