Università Roma Tre

Definition of a sigma-algebra; measures on a sigma-algebra; definition of the integral; monotone and dominated convergence theorems; continuity and derivation under the integral sign; the L^p spaces; Holder and Minkowski inequalities; L^p is complete; the Borel sets and Lusin's theorem; the compactly supported, C^\infty functions are dense in L^p(R^n); convergence in measure and almost-uniform convergence; Egorov's theorem; Caratheodory's extension theorem and the construction of Lebesgue's measure; product measures; the theorems of Fubini and Tonelli; complex measures; the Radon=Nykodim theorem and differentiation of measures.

W. Rudin, Real and complex analysis, Tata-McGraw Hill.

H. L. Royden, Real analysis, China Machine Press.

R. L. Wheeden, A. Zygmund, Measure and integral, Dekker.