Nível: Mestrado (Graduate level.).

Semestre: 2025/2

Tipo de curso: Curso regular do Programa de Verão (Summer School)

Content: Measurable functions, Lebesgue's Dominated Convergence Theorem, Basic Convergence Theorems, Riesz Representation Theorem, Lp Spaces, Completeness of Lp Spaces, Radon-Nikodym Measures, Integration on Product Spaces, Fubini`s Theorem, Lebesgue Differentiation Theorem

References:

• BARTLE, R. – The Elementos of Integration, NewYork, J. Wiley, 1966.

• FOLLAND, Gerald B. Real analysis : modern techniques and their applications, 1984 

• FERNANDEZ, P. – Medida e Integração. Rio de Janeiro, IMPA, Projeto Euclides, 1976.

• ISNARD, C. – Introdução à Medida e Integração. Projeto Euclides, IMPA, 2007.

• ROYDEN, M. – Real Analysis. New York, The MacMillan, 1963.

• RUDIN, W. – Real and Complex Analysis. New York, Mc-Graw Hill, 1966.

Course Material:

• Lista 1

• Lista 2

• Lista 3

• Lista 4

• Lista 5

• Lista 6

• Lista 7

• Prova 1

• Prova 2

NOTAS DE AULA - elaboradas por Juan Pablo L. T. de Melo a partir das aulas do semestre 2025 ministradas por mim. 

________________________________________________________________________________________________________________________________________

Nível: Mestrado (Graduate level.).

Semestre: 2021 (verão)

Tipo de curso: Curso regular do Programa de Verão (Summer School)

Content: Measurable functions, Lebesgue's Dominated Convergence Theorem, Basic Convergence Theorems, Riesz Representation Theorem, Lp Spaces, Completeness of Lp Spaces, Radon-Nikodym Measures, Integration on Product Spaces, Fubini`s Theorem, Lebesgue Differentiation Theorem