Construction of the Lebesgue measure, measurable functions, limit theorems. Lebesgue integration. Different notions of convergence and convergence theorems. Product measures and the Radon-Nikodym theorem, change of variables, complex measures.
De Berra, G., Introduction to Measure Theory, Von Nostrand Reinhold, 1974.
Hewitt, E. and Stromberg, K., Real and Abstract Analysis, Springer, 1969
Royden, H. L., Real Analysis, Macmillan, 1988.
Real and Complex Analysis, McGraw-Hill, 1986.