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.

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.

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.

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.