I want to find a sequence of measurable sets $A_k$.
such that $A_k \subset [0,1]$, $\lim \lambda(A_k) =1$, but $\liminf A_k = \varnothing$.
There are some examples on function such as $\sin x \over x$ , but I can't apply on a set, $A_k$.
Please give me a simple example.