Let $E= \cup _{k=1}^{\infty} E_k$ where all the sets $E_k$'s are measurable and $m(E)< \infty$. Suppose $f$ is bounded and integrable one every $E_k$.
Is $f$ integrable on $E$?
Let $E= \cup _{k=1}^{\infty} E_k$ where all the sets $E_k$'s are measurable and $m(E)< \infty$. Suppose $f$ is bounded and integrable one every $E_k$.
Is $f$ integrable on $E$?