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Lebesgue Integration - MAT00013H

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  • Department: Mathematics
  • Module co-ordinator: Dr. Zaq Coelho
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Spring Term 2017-18

Module aims

The Lebesgue integral is an extension of the Riemann integral studied in Real Analysis, able to integrate many more functions. This module aims to construct the Lebesgue integral on n-dimensional real space and demonstrate that it agrees with our intuitive idea of area under a graph, can be computed by familiar methods whenever they are applicable (anti-differentiation in one dimension, repeated one-dimensional integrals in higher dimensions), and is sufficiently wide in scope to give the powerful convergence theorems needed for more advanced applications.

Module learning outcomes

At the end of this module students should be able to understand:

The concept (definition and significance) of a null set in n-dimensional space;

the construction of the Lebesgue integral in terms of monotone sequences of step functions;

computation of Lebesgue integrals using the Fundamental Theorem of Calculus, Monotone and Dominated Convergence Theorems, and the Tonelli and Fubini Theorems.

Assessment

Task Length % of module mark
University - closed examination
Lebesgue Integration
2 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
University - closed examination
Lebesgue Integration
2 hours 100

Module feedback

Information currently unavailable

Indicative reading

A J Weir, Lebesgue Integration and Measure, Cambridge University Press.



The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.