MT5865 Measure Theory

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11am Monday (odd weeks), Wednesday, Friday

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof L O R Olsen

Prof L O R Olsen
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module introduces some of the powerful techniques and ideas of modern mathematical analysis that are important both in analysis in its own right and in its many applications in mathematics. The module will include topics such as: measure theory, integration theory and differentiation theory of measures. Mathematical analysis and the use of measure theory in analysis is one of the active research areas within the School, and the choice of topics will reflect current activity.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT3502

Anti-requisites

YOU CANNOT TAKE THIS MODULE IF YOU TAKE MT5825

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks), 1 tutorial (x 9 weeks)

Scheduled learning hours

34

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

119

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Understand the notion of a sigma-algebra and a measure
  • Understand the definition of the Lebesgue integral
  • Understand and appreciate the convergence results associated with the Lebesgue integral, including, the monotone convergence theorem and the dominated convergence theorem
  • Understand the definition and the theory of the Lebesgue spaces L^p
  • Understand the construction of product measures
  • Understand Radon-Nikodym’s theorem