# Stone-Weierstrass and an Alternative Proof of Itô's Lemma

In a similar sense to line integrals, stochastic calculus extends the classical tools to working with stochastic processes. One of the most elegant and useful result is the change of variable formula for stochastic integrals, commonly known as Itô’s Lemma (see end of this post for a discussion on Doeblin’s contribution). While this lemma is quite easy to use, the proof usually relies heavily on technical lemmas, hence difficult to develop intuition, especially for the first time reader.