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

Extracted text: Consider the decreasing sequence of functions {fn} defined on R, where fn(r) = X[n,00), Vn e N. That is, fn is the characteristic function of the interval [n, 0) for all n e N. Use the sequence {fn} as a counterexample to show that the Monotone Convergence Theorem does not hold for decreasing sequence of functions.