Let fn be integrable on [0, 1] and fn f uniformly on [0, 1]. Show that if bn f 1 as n , then limo,

Let fn be integrable on [0, 1] and fn †’ f uniformly on [0, 1]. Show that if bn f †‘ 1 as n †’ ˆž, then

limo, fn(x) dx= 10 f(x) dx.