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Academic Year 2020–2021 PhD in Statistics and Computer Science, Bocconi University

Real Analysis I Lecturer: Hugo Lavenant Prerequisites: undergraduate real analysis (familiarity with ε δ arguments, infinite series, basics of topology). Course description. The goal of the course is to cover measure theory and integration. The course will hopefully be useful for students whose research will involve rigorous proofs in probability theory, statistics and functional analysis. Course outline • σ-algebras and measurable functions. • Positive measures and integration. • Construction of measures. Radon measures on R and Lebesgue-Stieltjes integral. • L p spaces. • Product measures, Fubini-Tonelli theorem. • Signed measures and Radon-Nykodim theorem. Textbooks • W. Rudin, Real and Complex Analysis. McGraw-Hill Higher Education. • R. B. Ash and C. Doléans-Dade, Probability and Measure Theory. Academic Press.

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