An Introduction to Measure Theory (Tao)

First Edition
by Terence Tao

Terence Tao, An Introduction to Measure Theory, AMS GSM 126, 2011. The MATH5825 companion text. Tao develops the theory partly through the exercises themselves — Lebesgue measure from elementary measure, the integration convergence theorems, modes of convergence, differentiation theorems, product measures — with the exercises woven inline through the text rather than collected at section ends.

Solutions to every exercise live at Solutions to Tao’s An Introduction to Measure Theory.