Università Roma Tre

Measure theory, outer measures, construction of Borel measures.
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces.
Radon measures, regularity, positive linear functionals, Riesz representation theorem.
Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus.
Lp spaces, basic properties, dual spaces, density theorems.
Introduction to geometric measure theory

G. Folland - "Real Analysis" - Wiley