# Thread: Let f be a bounded measurable function on [a,b]...

1. ## Let f be a bounded measurable function on [a,b]...

Hi there. I am new here. I am really sorry to ask, but I have been hung up on this problem for a couple of days. I just don't understand what I am supposed to do. Sorry for the lack of Latex, but I think my writing is understandable. My problem is below. Thanks in advance.
Let f be a bounded measurable function on [a,b]. If A is a measurable subset of [a,b] with lambda(A) = 0, prove that integral of f d(lambda) = 0. (The subscript on the integral is A)

2. Hi

Remember that

$\left |\int_A f d\lambda \right| \leq \int_A |f| d\lambda \leq M \lambda(A) =0$

where $|f|\leq M$.