I recently read an article on probability theory that use the notation:
q(x) << p(x)
where p(x) and q(x) are two density functions of two distributions. What does the operator << mean in this context? I search around but cannot find the answer and they do not define this notation.
It's in this article: arxiv.org/pdf/1710.03266.pdf, e.g., theorem 3.1
In theorem 3.1, $p_{\theta}$ and $q_{\theta}$ are probability measures rather than density functions. That notation means $q_{\theta}$ is absolutely continuous w.r.t. $p_{\theta}$, i.e. if $p_{\theta}(A) = 0$ then $q_{\theta}(A) = 0$.