Assume F isn't increasing...then you have x<y with F(x)>F(y). Pick an epsilon smaller than half of |F(x)-F(y)|, and find an n such that f_n is within epsilon of F at both x and y.
I would like to know how to prove the following:
If fn converge pointwise to F on D and each fn is monotone increasing on D, then F is monotone increasing on D (and also for monotone decreasing).
Can someone please help me on this? Thank you!
( Do we have to make like a gn(x) = fn(x) - F(x) ...)