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Measure Theory (MAST90012)

Graduate courseworkPoints: 12.5Not available in 2024

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Overview

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Measure Theory introduces the modern conceptual framework of analysis that has led to a transformation and generalisation of such basic objects as functions, and such notions as continuity, differentiability and integrability.

It is fundamental to many areas of mathematics and probability and has applications in other fields such as physics and economics. Students will be introduced to the core topics of Lebesgue's theory of integration, and abstract measure theory, in particular signed measures, the Hahn-Jordan decomposition, the Radon-Nikodym derivative. Additional topics may include rudiments of probability theory (conditional expectation, Borel sets and measures) and geometric analysis (rectifiable curves, Hausdorff measure and dimension).

Intended learning outcomes

On completion of this subject, students will:

  • Understand the fundamentals of measure theory and be acquainted with the proofs of the fundamental theorems underlying the theory of integration;
  • Understand how these underpin the use of mathematical concepts such as volume, area, and integration;
  • Develop a perspective on the broader impact of measure theory in ergodic theory; and
  • Have the ability to pursue further studies in this and related areas.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • Problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • Analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • Collaborative skills: the ability to work in a team;
  • Ttime-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 31 January 2024