Measure and Integration (L.7) (850G1)
Measure and Integration (L.7)
Module 850G1
Module details for 2022/23.
15 credits
FHEQ Level 7 (Masters)
Module Outline
This module provides a rigorous introduction to measure theory and Lebesgue integration. We will study measures and their properties, learn to construct measures from outer measures using Caratheodory's method, and construct the Lebesgue measure on the line. We will then develop the powerful concept of Lebesgue integral and make the use of it by mastering convergence theorems. The last part of the module gives an introduction to L^p spaces.
Module learning outcomes
A successful student should: know the concept and the properties of a sigma-additive measure;
understand how the concepts of integral and measure are related;
be able to state and apply central results of integration theory such as: monotone and dominated convergence theorems or theorems on parameter-dependent integrals;
know basic facts on L^p spaces.
| Type | Timing | Weighting |
|---|---|---|
| Computer Based Exam | Semester 1 Assessment | 80.00% |
| Coursework | 20.00% | |
| Coursework components. Weighted as shown below. | ||
| Portfolio | T1 Week 11 | 40.00% |
| Problem Set | T1 Week 4 | 15.00% |
| Problem Set | T1 Week 6 | 15.00% |
| Problem Set | T1 Week 9 | 15.00% |
| Problem Set | T1 Week 11 | 15.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Autumn Semester | Lecture | 2 hours | 11111111111 |
| Autumn Semester | Lecture | 1 hour | 11111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Vladislav Vysotskiy
Convenor, Assess convenor
/profiles/406081
Please note that the University will use all reasonable endeavours to deliver courses and modules in accordance with the descriptions set out here. However, the University keeps its courses and modules under review with the aim of enhancing quality. Some changes may therefore be made to the form or content of courses or modules shown as part of the normal process of curriculum management.
The University reserves the right to make changes to the contents or methods of delivery of, or to discontinue, merge or combine modules, if such action is reasonably considered necessary by the University. If there are not sufficient student numbers to make a module viable, the University reserves the right to cancel such a module. If the University withdraws or discontinues a module, it will use its reasonable endeavours to provide a suitable alternative module.