In the paper Wherefor Art Thou R3579X? they state at the end of page 5, while proving theorem 2.2, that "Once $j$ is $\Theta(\log \log n)$, each term in the sum is $O(1)$".
My question is now what does "Once $j$ is $\Theta(\log \log n)$" mean? Does this have a proper definition or is it just more abuse of asymptotic notation?