This is from my recent homework. I am asked to find a descending nested sequence of closed , bounded , nonempty convex sets $\{D_n\}$ in $L^1(\mathbb{R})$ such that the intersection is empty , where elements in $D_n$ should be integrable functions defined on R.
There is a discussion on mathoverflow which says we could replace unit ball part in James theorem by convex closed set . As suggested in the comments , possibly this is needed for the question.
Could anyone help me with this ?