Hi everyone.

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

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

Thanks for your Help