Given a countable collection of measurable sets, is it possible to construct a new collection of sets which are pairwise disjoint and have the same union as the original? Yes! Here's the trick....

This post is the sixth example in an ongoing list of various sequences of functions which converge to different things in different ways. Today we have a sequence of functions on $[0,1]$ which converges to 0 in $L^1$, but does not converge anywhere on $[0,1]$.

This week we continue our discussion on the Stone Weierstrass Theorem with an example. This exercise is taken from Rudin's Principles of Mathematical Analysis (affectionately known as "Baby Rudin"), chapter 7 #20.