MATE-4220 Medida e Integración

Algebras and sigma-algebras, measures, Lebesgue Measure, Constitution and regularity. integrated functions: Roles measurable properties almost everywhere, the definition of integral, theorems of boundaries, Riemann integral, complex functions and extent of image. Convergence: Modes of convergence, regulated spaces, Lp spaces, dual spaces. Real and complex measures: Absolute continuity, singularity, functions of bounded variation, dual spaces Lp. Product measures: construction, Fubini Theorem, applications.