**Real Analysis I**

*“F just comes along for the ride…”*

**Text: **Real Analysis: Modern Techniques and Their Applications by Gerald B. Folland

**Prof:** Dr Stephen Gustafson

Prof Gustafson is an engaging professor. He is able to give a quick, intuitive overview of quite complex topics in class, leaving us to work out the technical details on our own. He also is very helpful during office hours. He also posted his notes online.

**Difficulty**

The classes move very fast so one might find it challenging keeping up with the readings. Also, though the classes are easy to follow, the homework is increasingly challenging and time-consuming. The final exam was quite hard, practice and recalling theorems and definitions are all important. This course covers a lot of material, so watch out!

** Key Concepts**

Sigma-Algebras

Measures

Differentiation of Measures

Lebesgue integration

Convergence of Functions

LP spaces

**Hard Concepts**

Lebesgue Radon Nikodyn Theorem: Quite powerful theorem, need to notice where to apply it. Also can be hard to find the decomposition at times.

Fatou’s Lemma: Tricky working with the limit infimum, also quite powerful and pops up in unexpected places.

**Conclusion**

One of the harder courses I have ever taken. Started learning some really powerful theorems about convergence, for example.