The above argument shows that for every sequence {δ"n"} → 0, the sequence formula_72 is uniformly bounded and converges pointwise to "f""x". The bounded convergence theorem states that if a sequence of functions on a set of finite measure is uniformly bounded and converges pointwise, then passage of the limit under the integral is valid. In particular, the limit and integral may be exchanged for every sequence {δ"n"} → 0. Therefore, the limit as δ → 0 may be passed through the integral sign.