Suppose in an atomless space, $f\in L^1$ and $||f||_1=1$
I want to prove there exists $g$ and $h$, $g\neq h$, such that $||g||_1=||h||_1=1$ and $f=(1-\lambda)g+\lambda h, 0 \lt \lambda \lt 1$
I'm not sure how to start this question, any tips would be greatly appreciated