Math 23b. Week 7, Video 3: The Ascoli-Arzela Theorem (20.4)

A discussion of the proof structure and key elements of the Ascoli-Arzela Theorem.

**NOTE** The Ascoli-Arzela Theorem is your proof 20.1 (proof that there exists a convergent subsequence that converges to a continuous function.
The fact that the convergence is UNIFORM is separately Proof 20.2.

[jameschen]

Big props! I'm studying for my grad qual and this helped me immensely!

[jameschen]

At the end, shouldn't we be using uniform equicontinuity instead of just uniform continuity? Otherwise we can't guarantee on a sequence of continuous functions that the 1/K is small enough for all of the f_{n, n} if n >= K.