I have no clue about the first one

For question #2:

I'm not sure what M is? Is that the domain of the function? Assuming it is

Let = {x \in M: f(x) > L }

Notice that and thus

Since f is integrable, the numerator is bounded and it follows that as L tends to infinity, tends to 0.

I'll leave it up to you to show that as and so we can find an L large enough such that and so the set we are looking for is E = M \

Note, this used the fact that we can break the integral up into disjoint sets.