MX4083: MEASURE THEORY (2021-2022)

Last modified: 31 May 2022 13:05

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
Term	First Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	Aberdeen	Sustained Study	No
Co-ordinators	Professor Benjamin Martin

Qualification Prerequisites

Programme Level 4

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

Any Undergraduate Programme (Studied)
MA2009 Analysis I (Passed)
MA1511 Set Theory (Passed)
MA2509 Analysis II (Passed)

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?

Course Description

Syllabus

Lebesgue extension of a measure; Extension a measure from a semi-ring of sets to the corresponding ring of sets; Algebras and σ-algebras of sets; σ-additive and σ-semi-additive measures;
Measure spaces; Lebesgue extension of a measure defined on a ring of sets; Properties of the Lebesgue measure.
Measurable functions; Definition and properties of measurable functions; Convergence almost everywhere; Measurable functions and uniform convergence; the Egorov theorem.
Lebesgue integral; Lebesgue integral for simple functions; The definition and the properties of the Lebesgue integral; Absolute continuity and σ-additivity of the Lebesgue integral; the Chebyshev inequality; The Lebesgue, the Levi and the Fatou convergence theorems for the Lebesgue integral; Comparison of the Lebesgue integral and of the Riemann integral.

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 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

Alternative Assessment

3x Assignments (33% each)

Alternative Resit Assessment

Resubmission of failed elements (pass marks carried forward).

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge Level	Thinking Skill	Outcome
Factual	Remember	ILO’s for this course are available in the course guide.