# Tuesday October 15

## Proof of Fubini's Theorem

Recall the strong version of DCT: 
It allows you to deduce $L^1$ converges from a.e. convergence. 

Note that otherwise, this are incomparable!

*Proof of Fubini's Theorem*: see book for the gory details.

> Essentially uses MCT a number of times and reduces to the case of cubes that possibly include boundaries.