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Notes on Measure and Integration

Author: John Franks
Url: http://arxiv.org/abs/0802.4076v3
Format: Ps, Pdf
Year: 2008
Category: Differential Equations
Pages: 118
Clicks: 956

This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of L2 functions on the interval. The actual construction of Lebesgue measure and proofs of its key properties are relegated to an appendix. Instead the text introduces Lebesgue measure as a generalization of the concept of length and motivates its key properties: monotonicity, countable additivity, and translation invariance.

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