Let on for all and on
Show that ther does not exist a set of measure zero ,on the complement of which is uniformly convergent.
Your functions are converging pointwise to the zero function. If you had some set as above, then you'd need, for any , that there exists some so that on for all . But if has measure zero, then the complement contains points arbitrarily near zero, i.e. points such that for as large as you like, which contradicts uniform convergence.