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  4. 2016-2017
  5. Mathematical Sciences
  6. MX4083: MEASURE THEORY

MX4083: MEASURE THEORY (2016-2017)

Last modified: 28 Jun 2018 10:27


Course Overview

Measure theory provides a systematic framework to the intuitive concepts of the length of a curve, the area of a surface or the volume of a solid body. It is foundational to modern analysis and other branches of mathematics and physics.




Course Details

Study Type Undergraduate Level 4
Session First Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Alexey Sevastyanov

Qualification Prerequisites

None.

What courses & programmes must have been taken before this course?

  • MX3021 Further Real Analysis (Passed)
  • Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

  • Sigma-algebras, measures, measurable functions.
  • The integral of simple, positive, measurable functions and hence of positive measurable functions.
  • Monotone Convergence Theorem.
  • Integrable functions, Fatou's Lemma, the Dominated Convergence Theorem and applications.
  • Comparison of Riemann, Cauchy-Riemann and Lebesgue integrals.
  • The Lebesgue L^p-spaces.
  • Discussion of the Tonelli and Fubini theorems, with applications to continuous functions of two real variables.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%). Resit: If required and permitted by Regulations, there will be 1 two-hour written examination. The CAS mark will be based on the maximum of examination (100%) and examination (80%) together with in-course assessment (20%).

Only the marks obtained on first sitting can be used for Honours classification.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinators for feedback on the final examination.

Course Learning Outcomes

None.
 

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