If converges almost everywhere to , then there is a zero set of points on which it does not converge. A zero set has certain properties. For one thing, it has measure zero. So, if , then you are guaranteed that the measure will be zero. So, let's construct . Since the zero set is a subset of , by the well ordering principle of real numbers, there exists a greatest lower bound of . Can you find a really small interval that will include , but not ? Will that interval be measurable? How do you know? Will converge to uniformly on that interval? Again, how do you know?