6. (10 points) Let fn:[0,1] →R,
, be a sequence of increasing functions, i.e., fn(x) ≤fn(y) for all
and n
N. Assume that fn Sfnt1 and Ifn(x)I s 1 for all xe [0,1] and neN. Show that fn converges (pointwisely) to an increasing function.
6. (10 points) Let fn:[0,1] →R,
, be a sequence of increasing functions, i.e., fn(x) ≤fn(y) for all
and n
N. Assume that fn Sfnt1 and Ifn(x)I s 1 for all xe [0,1] and neN. Show that fn converges (pointwisely) to an increasing function.