Real And Functional Analysis – Politecnico di Milano

Argomenti del programma: 1. Real Analysis. Measurable space, measure, outer measure. Generation of an outer measure. Carathéodory's condition, measure induced by an outer measure. Lebesgue's measure on R ^n. Measurable functions. The Lebesgue integral. Abstract integration. Monotone convergence theorem, Fatou's Lemma, Lebesgue's dominated convergence theorem. Comparison between the Lebesgue and Riemann integrals.

Argomenti del programma: 1. Real Analysis. Measurable space, measure, outer measure. Generation of an outer measure. Carathéodory's condition, measure induced by an outer measure. Lebesgue's measure on R ^n. Measurable functions. The Lebesgue integral. Abstract integration. Monotone convergence theorem, Fatou's Lemma, Lebesgue's dominated convergence theorem. Comparison between the Lebesgue and Riemann integrals.

Argomenti del programma: 1. Real Analysis. Measurable space, measure, outer measure. Generation of an outer measure. Carathéodory's condition, measure induced by an outer measure. Lebesgue's measure on R ^n. Measurable functions. The Lebesgue integral. Abstract integration. Monotone convergence theorem, Fatou's Lemma, Lebesgue's dominated convergence theorem. Comparison between the Lebesgue and Riemann integrals.