20410876 - AM400 - ELEMENTS OF ADVANCED ANALYSIS

To acquire a good knowledge of the abstract integration theory and of the functional spaces L^p.

Curriculum

scheda docente | materiale didattico

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" - Wiley

Modalità Erogazione

Lectures.

Modalità Frequenza

Attending classes is not mandatory but it is strongly advised

Modalità Valutazione

Homework (three overall assignments) and oral exam about the course's program.

scheda docente | materiale didattico

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" - Wiley

Modalità Erogazione

Lectures.

Modalità Frequenza

Attending classes is not mandatory but it is strongly advised

Modalità Valutazione

Homework (three overall assignments) and oral exam about the course's program.

scheda docente | materiale didattico

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" - Wiley

Modalità Erogazione

Lectures.

Modalità Frequenza

Attending classes is not mandatory but it is strongly advised

Modalità Valutazione

Homework (three overall assignments) and oral exam about the course's program.