I am trying to solve this problem:
If $f : \mathbb{R} \to \mathbb{R}$ is a Lebesgue measurable function and $\int_{0}^{1}{f(x)dx} = 1$ (Lebesgue integral) and $E = \{x \in [0, 1] \mid f(x) > 1\}$, then what is the value of the Lebesgue integral $\int_{E}{(f(x) - 1) dx}$?
But I haven't reached any good results