Official Course Description
In this course we introduce a more general integral concept, the so called Lebesgue integral, that extends to a larger class of functions. The Lebesgue integral is a generalization of the usual Riemann integral that allows easier rules for integration of limits of sequences of functions and it is an important tool in modern analysis. Integrals with respect to general measures play a crucial role in many branches of mathematics, as real analysis, the theory of probability and potential theory. The course comprises basic measure theory, construction of the Lebesgue measure, convergence theorems and Fubini's theorem.