We know for an integrable function $f$, if $\int_\mathbb{R} f=1$, then $\forall \lambda\in [0,1] $, there exists a measurable set $E$ that $\int_E f=\lambda$.

Now consider integrable functions $f$ and $g$, if $\int_\mathbb{R} f=1=\int_\mathbb{R} g$, then $\forall \lambda\in [0,1] $, does there exist a measurable set $E$ that $\int_E f=\lambda=\int_\mathbb{E} g$?