Edit: I just realized, it would probably help to clarify if you're unfamiliar - the reason the above are sensible notions of limsup and liminf is because they're $\bigcap_{n\in\mathbb{N}} \bigcup_{k=n}^\infty A_k$ and $\bigcup_{n\in\mathbb{N}} \bigcap_{k=n}^\infty A_k$, respectively.