# Measure Theory and Fourier Analysis (Adv) (MATH3969)

## UNIT OF STUDY

Measure theory is the study of such fundamental ideas as length, area, volume, arc length and surface area. It is the basis for the integration theory used in advanced mathematics since it was developed by Henri Lebesgue in about 1900. Moreover, it is the basis for modern probability theory. The course starts by setting up measure theory and integration, establishing important results such as Fubini's Theorem and the Dominated Convergence Theorem which allow us to manipulate integrals. This is then applied to Fourier Analysis, and results such as the Inversion Formula and Plancherel's Theorem are derived. The Radon-Nikodyn Theorem provides a representation of measures in terms of a density. Probability theory is then discussed with topics including distributions and conditional expectation.

## Further unit of study information

### Classes

Three 1 hour lectures and one 1 hour tutorials per week.

### Assessment

One 2 hour exam, assignments, quizzes (100%)

### Faculty/department permission required?

No

## Unit of study rules

### Prerequisites and assumed knowledge

Credit average or greater in 12 credit points Intermediate Mathematics, Credit average or greater in 12 credit points Intermediate Mathematics, Credit average or greater in 12 credit points Intermediate Mathematics

At least 6 credit points of (Intermediate Advanced Mathematics or Senior Advanced Mathematics units)

### Prohibitions

MATH3909, MATH3909, MATH3909

## Study this unit outside a degree

### Non-award/non-degree study

If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student.

### Cross-institutional study

If you are from another Australian tertiary institution you may be permitted to underake cross-institutional study in one or more units of study at the University of Sydney.