On Jun 17, 12:52 pm, Mark Dickinson <dicki... at gmail.com> wrote: > g_n(t) = nt if 0 <= t <= 1/n else 1 Whoops. Wrong definition. That should be: g_n(t) = nt if 0 <= t <= 1/n else n(2/n-t) if 1/n <= t <= 2/n else 0 Then my claim that g_n(t) -> 0 for all t might actually make sense...