Measure And Integration

Extension
theorems of measures and integrals. Basic theorems of convergence. Signed measures. Hahn-Jordan decomposition theorem. Absolutely continuous measures. Lebesgue’s decompostion theorem. Radon-Nikodym theorem. Lp-spaces: basic properties; duality. Product spaces. Fubini-Tonelli theorem. Riesz-Markov representation theorem. Convergence in measure. Differentiation and integration: Vitali’s theorem; Lebesgue’s differentiation theorem.

References:
ARMANDO CASTRO JR, A. – Curso de Teoria da Medida. Rio de janeiro, IMPA, Projeto Euclides, 2ª. ed., 2008.
BARTLE, R. – The Elementos of Integration, New York, J. Wiley, 1966.
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.