2224

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2224: Lebesgue Measure

Lecturer: Prof. Richard M. Timoney

Website: Link

1 Introduction
2 The course
3 The subject
4 Resources

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Introduction

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The course

The course begins with the concepts of countability and boolean algebras of sets. The idea of a measure as a rigorous extension of length, area, volume &c is introduced, followed by the extension of the natural length subset of $\mathcal{P}(\mathbb{R}^n)$ - the interval algebra - to that of Lebesgue measurable sets through the definition of the outer measure and Carathéodory's criterion. These conceptual extensions of length, and most notable that of a set having measure zero, lead directly to a far broader and more satisfying definition of integration than Riemann's.