## MA4MTI-Measure Theory and Integration

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites: MA2RCA Real and Complex Analysis or MA3RCA Real and Complex Analysis
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3MTI Measure Theory and Integration
Current from: 2021/2

Module Convenor: Dr Nikos Katzourakis

Type of module:

Summary module description:

This module provides an introduction to measure theory and integration.

Aims:

The course gives an introduction to the general measure theoretical approach to integration. A unified approach to the concepts of length, area and integral is given.

Assessable learning outcomes:

By the end of the course, students are expected to:

• have a deep understanding of the concepts of measure, measurability and integral for general measure spaces, and be able to solve problems involving these;

• have a deep understanding of limiting processes with Lebesgue integrals and be able to handle these rigorously.

This module will be assessed to a greater depth than the excluded module MA3MTI.

Students should develop an understanding of the concepts of area, length and general measure theory. They should reflect on the difference, advantages and disadvantages of Riemann versus Lebesgue integration.

Outline content:

Measurable sets, measure, construction of measures, measure zero sets, measurable functions, construction of the integral, properties which hold almost everywhere, and limit theorems.

Brief description of teaching and learning methods:

Lectures supported by lecture notes, non-assessed problem sheets with solutions and guided independent study.

Contact hours:
 Autumn Spring Summer Lectures 20 Guided independent study: 80 Total hours by term 100 Total hours for module 100

Summative Assessment Methods:
 Method Percentage Written exam 100

Summative assessment- Examinations:

2 hour examination

Summative assessment- Coursework and in-class tests:

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

A mark of 50% overall.

Reassessment arrangements:

Oral examination/presentation.