Does not exist.
Measurable sets and measurement spaces. Construction of measures. Measurement extensions, Caratheodory Theorem. Lebesgue and Lebesgue-Stieltjes measure. Measurable Functions. Simple functions. Lebesgue integral. Monotonous convergence theorem, Fatou's lemma and dominated convergence theorem. Comparison between Riemann and Lebesgue integrals. Lp spaces. Holder inequality and Minkowski inequality; Completeness of Lp spaces. Average convergence, uniform in almost every point and in Lp. Comparison between the types of convergence. Radon-Nikodym theorem. Product measures and Fubini's theorem. Probability and conditional expectation.
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· Bartle. The Elements of Integration and Lebesgue Measure. Wiley.
· Pedro J. Fernandez. Measure and Integration. Euclides Collection, IMPA.
· Resnick. The Probability Path. Springer.
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· Castro Junior. Measure Theory Course. Euclides Project, IMPA.
· Carlos Isnard. Introduction to Measure Theory. Euclides Project, IMPA.