Lebesgue Measure and Integration

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Lebesgue Measure and Integration

Credits

6

Prerequisites

Mathematical Analysis 2.

Scientific-disciplinary sector (SSD)

MAT/05 Mathematical Analysis.

 

Examination method

Passing an oral exam.

Learning
objectives

The course aims to provide an introduction to the theory of partial differential equations of mathematical physics. Students learn methods for the study of well-posed problems relating to such equations.

Contents

Measure spaces. Measurable sets. The Peano-Jordan measure and the Lebesgue measure in Euclidean space. Measurable functions. Convergence of measurable functions. Integral of a measurable function. The Lebesgue integral and its properties. The Radon-Nikodym theorem. Passage to the limit under the integral sign. Product measure spaces. The space of p-th power summable functions. The indefinite Lebesgue integral. Absolutely continuous functions. The Cantor function.