Consider the decreasing sequence of functions {f„} defined on R, where fn(x) = X[n,00), Vn e N. That is, f, is the characteristic function of the interval [n, 0) for all n e N. Let f = 0 on R or f(r)...

Proving:

Extracted text: Consider the decreasing sequence of functions {f„} defined on R, where fn(x) = X[n,00), Vn e N. That is, f, is the characteristic function of the interval [n, 0) for all n e N. Let f = 0 on R or f(r) = 0 for any r e R. Show that fn + f pointwise on R, that is, lim fn(r) = 0, Vr e R. %3D