Inferior limit when t decreases to 0

Question

I just found in a book, the notation (for a real valued function $f$) $$ \liminf_{t \searrow 0} f(t)$$ I know what $$\liminf_{t\to 0} f(t)$$ means: $$\liminf_{t\to 0} f(t) = \lim_{\epsilon \to 0} \left(\inf_{s\in [-\epsilon,\epsilon]} f(s)\right)$$ but how can I define $$ \liminf_{t \searrow 0} f(t) ?$$ Is it equivalent to $$ \lim_{\epsilon \to 0,\epsilon >0} \left(\inf_{s\in [0,\epsilon]} f(s)\right)?$$