Given pointwise on a domain , where each is monotone (either increasing or decreasing) on , show that is monotone on .
so what I have is:
assume that f_n(x) is monotone increasing then:
by definition (the one that I am using) a function is pointwise convergent if and only if and if and only if given an (dependent on both and ) such that
so based on that if I let:
hence as increase so does
is this correct?