Learning objectives
To provide basic knowledge of measure theory and integration in its abstract formulation.
Prerequisites
Mathematical Analysis courses of the specialistic degree. Elements of topology.
Course unit content
Abstract integration. Positive Borel measures. Lebesgue measure. Lebesgue spaces and inequalities. Signed measure. Integration on product spaces and Fubini's theorem. Product measure. Fourier transform.
Full programme
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Bibliography
Walter Rudin, Real and Complex Analysis.
Teaching methods
Lectures with theory and exercises. Written test (exercises). Oral test (discussion of the written test and verification of the theoretical knowledge of the contents of the course).
Assessment methods and criteria
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Other information
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