MATH40430 Measure Theory & Integration

Academic Year 2023/2024

Measure theory simply seeks to assign a measure, or quantity, to certain sets (typically in R^n) which is consistent, reasonably general, and agrees with our intuition in familiar situations. With this, one can develop the Lebesgue theory of integration which has several advantages over the rather limited Riemann integral. The material is fundamental to modern analysis, particularly stochastic processes and the mathematical models of financial markets.

Show/hide contentOpenClose All

Curricular information is subject to change

Learning Outcomes:

On successful completion of this module the student should appreciate the shortcomings in the Riemann integral and the necessity for the introduction of the Lebesgue integral; be familiar with the basic theory of sigma algebras,
measurable functions and integrable functions; know the conditions under which it is possible to swap limits and integration; be familiar with applications of measure theory to functional analysis, potential theory and other areas of mathematics.

Student Effort Hours: 
Student Effort Type Hours
Lectures

30
Tutorial

6
Specified Learning Activities

24
Autonomous Student Learning

60
Total

120
Approaches to Teaching and Learning:
. 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Pre-requisite:
MATH10320 - Mathematical Analysis

Incompatibles:
MATH30360 - Measure Theory & Integration, MATH40790 - Measure Theory (online)

Additional Information:
Students should have completed a first course on mathematical analysis, such as MATH10320, which provides familiarity with concepts such as the completeness axiom, uniform convergence of functions, cardinality of sets and "epsilon-delta" arguments.


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: End of Semester (2hr) 2 hour End of Trimester Exam No Graded No

80
Continuous Assessment: Homework Throughout the Trimester n/a Graded No

20

Carry forward of passed components
No
 
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Autumn
      
Lecture Offering 1 Week(s) - Autumn: All Weeks Fri 15:00 - 15:50
Lecture Offering 1 Week(s) - Autumn: All Weeks Thurs 15:00 - 15:50
Lecture Offering 1 Week(s) - Autumn: All Weeks Tues 16:00 - 16:50
Autumn