I will write a question from Folland's book. What I want to ask is not the solution of this problem, but the way how to approach it. Question is as follows:
If $f \in L^+$ and $\int f < \infty$, for every $\epsilon > 0$ there exists $E \in \mathcal{M}$ such that $\mu(E) < \infty$ and $\int_E f > (\int f) - \epsilon$.
So as I said, I simply need to understand the approach I should take. For instance, what does the last inequality mean? What it says when you write a statement like $b > a - \epsilon$?
Also, I want to gain intuition about the way of full solution. Thanks.