20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS

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

BATTAGLIA LUCA

teacher profile | teaching materials

Mutuazione: 20410409 AM310 - ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA, ESPOSITO PIERPAOLO

Programme

Measure theory, outer measures, construction of Borel measures and the Lebesgue measure.
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces, change of variables for the Lebesgue integral.
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.

Core Documentation

G. Folland - "Real Analysis" - Wiley

Type of delivery of the course

Lectures.

Type of evaluation

Homework and oral exam.

ESPOSITO PIERPAOLO

teacher profile | teaching materials

Mutuazione: 20410409 AM310 - ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA, ESPOSITO PIERPAOLO

Programme

Measure theory, outer measures, construction of Borel measures and the Lebesgue measure.
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces, change of variables for the Lebesgue integral.
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.

Core Documentation

G. Folland - "Real Analysis" - Wiley

Type of delivery of the course

Lectures.

Type of evaluation

Homework and oral exam.

BATTAGLIA LUCA

teacher profile | teaching materials

Mutuazione: 20410409 AM310 - ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA, ESPOSITO PIERPAOLO

Programme

Measure theory, outer measures, construction of Borel measures and the Lebesgue measure.
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces, change of variables for the Lebesgue integral.
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.

Core Documentation

G. Folland - "Real Analysis" - Wiley

Type of delivery of the course

Lectures.

Type of evaluation

Homework and oral exam.

ESPOSITO PIERPAOLO

teacher profile | teaching materials

Mutuazione: 20410409 AM310 - ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA, ESPOSITO PIERPAOLO

Programme

Measure theory, outer measures, construction of Borel measures and the Lebesgue measure.
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces, change of variables for the Lebesgue integral.
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.

Core Documentation

G. Folland - "Real Analysis" - Wiley

Type of delivery of the course

Lectures.

Type of evaluation

Homework and oral exam.

BATTAGLIA LUCA

teacher profile | teaching materials

Mutuazione: 20410409 AM310 - ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA, ESPOSITO PIERPAOLO

Programme

Measure theory, outer measures, construction of Borel measures and the Lebesgue measure.
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces, change of variables for the Lebesgue integral.
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.

Core Documentation

G. Folland - "Real Analysis" - Wiley

Type of delivery of the course

Lectures.

Type of evaluation

Homework and oral exam.

ESPOSITO PIERPAOLO

teacher profile | teaching materials

Mutuazione: 20410409 AM310 - ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM-40 BATTAGLIA LUCA, ESPOSITO PIERPAOLO

Programme

Measure theory, outer measures, construction of Borel measures and the Lebesgue measure.
Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces, change of variables for the Lebesgue integral.
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.

Core Documentation

G. Folland - "Real Analysis" - Wiley

Type of delivery of the course

Lectures.

Type of evaluation

Homework and oral exam.