In the probability theory, $f \asymp g$ as $p\to \pi$ if $$\frac{f(p)}{g(p)}$$ is bounded away from 0 and $\infty$ on a neighbourhood of $\pi$.
But in the analysis, \begin{align} f(x) \asymp g(x) \implies \exists c_1,c_2, \text{ such that}\\ c_1|g(x)|\leq |f(x)| \leq c_2|g(x)| \end{align}
How to show that these two definitions are equivalent?