To acquire a good knowledge of the abstract integration theory and of the functional spaces L^p.
Curriculum
teacher profile teaching materials
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
Programme
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
Core Documentation
G. Folland - "Real Analysis" - WileyType of delivery of the course
Lectures.Type of evaluation
Homework (three overall assignments) and oral exam about the course's program. teacher profile teaching materials
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
Programme
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
Core Documentation
G. Folland - "Real Analysis" - WileyType of delivery of the course
Lectures.Type of evaluation
Homework (three overall assignments) and oral exam about the course's program. teacher profile teaching materials
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
Programme
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
Core Documentation
G. Folland - "Real Analysis" - WileyType of delivery of the course
Lectures.Type of evaluation
Homework (three overall assignments) and oral exam about the course's program.