1. The problem statement, all variables and given/known data Show that there exists measurable functions f_n defined on some measure subspace, st f_n-> f a.e. but such that f is not measurable. 2. Relevant equations Converges a.e. means that converges everywhere except on a set of measure zero. 3. The attempt at a solution Need to construct a measure space in which some subset of a measurable set of measure zero is not measurable. However, such measure space is not compelte.