Lebesgue measure and integration

This page hosts a set of notes that I wrote to introduce my Real Analysis students to Lebesgue measure and Lebesgue integration.

These notes extend Jay Cumming's Real Analysis Long-Form Math textbook and are meant to be used after Chapter 8 (Darboux integration). The notes contain two chapters:

• Chapter 10 covers Lebesgue measure and measurable functions

• Chapter 11 covers Lebesgue integration from a simple functions viewpoint.

 The notes are embedded below, or you can access the PDF directly using this link:

Download Lebesgue notes

These notes are free for you to use. If you use them, please drop me an email to let me know how it goes, report errors, etc.

The notes are currently in Beta edition: They've been used and revised but are likely to still have some typos or errors.