How to prove this? Please help me. Thank you very much.
A measurable set $E$ in a measure space $(X, \mathcal{M}, \mu)$ is said to be an atom if $\mu (E) > 0$ and no proper measurable subset of $E$ has positive $\mu$ measure.
Let $(X, \mathcal{M}, \mu)$ be a $\sigma$- finite measure space. Prove that the set of extreme points in $B_{L^1(\mu)}=\{v \in L^1(\mu): \|v\| \le 1\}$ is equal to $\{\pm \mu(F)^{-1} \chi_F: F \mbox{ is an atom of }\mu\}$.