# MATH40790 Measure Theory (online)

## Academic Year 2022/2023

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.

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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
Specified Learning Activities

24

Autonomous Student Learning

60

Online Learning

36

Total

120

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Requirements:

A first course in Mathematical Analysis equal or equivalent to MATH10320 is required.

Learning Recommendations:

It is recommended that students have taken first courses in Calculus and Metric Spaces, equal or equivalent to MATH10350 and MATH30090, respectively.

Module Requisites and Incompatibles
Incompatibles:
MATH30360 - Measure Theory & Integration, MATH40430 - Measure Theory & Integration

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Continuous Assessment Throughout the Trimester n/a Standard conversion grade scale 40% No

20

Examination: Written examination. 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

80

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour