Measure Theory Problem

Hi everyone.
I´ve this problem in measure theory, but I dont know how to treat it.

Let $(X,A, \mu )$ be a measure space where $\mu(X) = 1$ and for all $E \in A, \mu(E) = 0$ or $\mu(E) = 1$. Let $f: X \rightarrow \mathbb{R}$ be a measurable function. Then exists $c \in \mathbb{R}$ such that $f(x) = c$ almost everywhere.