In some contexts one encounters statements like:
The following equation is true $$ f(x) = o(g(x)), $$ when $x\to\infty$ outside of an exceptional set $E$ of such and such measure.
My interpretation is that the statement above means that there exists a set $E$ of such and such measure, such that $$ f|_{E^\complement}(x) = o(g(x)), $$ where $x\to\infty$. Is this accurate?