To acquire a good knowledge of the abstract integration theory and of the functional spaces L^p.
Curriculum
scheda docente
materiale didattico
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces.
Radon measures, regularity, positive linear functionals, Riesz representation theorem.
Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus.
Lp spaces, basic properties, dual spaces, density theorems.
Introduction to geometric measure theory
Mutuazione: 20410876 AM400-ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA
Programma
Measure theory, outer measures, construction of Borel measures.Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces.
Radon measures, regularity, positive linear functionals, Riesz representation theorem.
Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus.
Lp spaces, basic properties, dual spaces, density theorems.
Introduction to geometric measure theory
Testi Adottati
G. Folland - "Real Analysis" - WileyModalità Erogazione
Lectures.Modalità Frequenza
Attending classes is not mandatory but it is strongly advisedModalità Valutazione
Homework (three overall assignments) and oral exam about the course's program.
scheda docente
materiale didattico
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces.
Radon measures, regularity, positive linear functionals, Riesz representation theorem.
Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus.
Lp spaces, basic properties, dual spaces, density theorems.
Introduction to geometric measure theory
Mutuazione: 20410876 AM400-ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA
Programma
Measure theory, outer measures, construction of Borel measures.Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces.
Radon measures, regularity, positive linear functionals, Riesz representation theorem.
Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus.
Lp spaces, basic properties, dual spaces, density theorems.
Introduction to geometric measure theory
Testi Adottati
G. Folland - "Real Analysis" - WileyModalità Erogazione
Lectures.Modalità Frequenza
Attending classes is not mandatory but it is strongly advisedModalità Valutazione
Homework (three overall assignments) and oral exam about the course's program.
scheda docente
materiale didattico
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces.
Radon measures, regularity, positive linear functionals, Riesz representation theorem.
Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus.
Lp spaces, basic properties, dual spaces, density theorems.
Introduction to geometric measure theory
Mutuazione: 20410876 AM400-ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA
Programma
Measure theory, outer measures, construction of Borel measures.Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces.
Radon measures, regularity, positive linear functionals, Riesz representation theorem.
Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus.
Lp spaces, basic properties, dual spaces, density theorems.
Introduction to geometric measure theory
Testi Adottati
G. Folland - "Real Analysis" - WileyModalità Erogazione
Lectures.Modalità Frequenza
Attending classes is not mandatory but it is strongly advisedModalità Valutazione
Homework (three overall assignments) and oral exam about the course's program.