Abstract
This chapter presents a geometric theory of Lebesgue measure and integration. In calculus you certainly learned that the integral is the area under the curve. With a good definition of area, that is the point of view we advance here. Deriving the basic theory of Lebesgue integration then becomes a matter of inspecting the right picture. See Appendix C for the relation between Riemann integration and Lebesgue integration.KeywordsDensity PointCountable UnionOuter MeasureOpen RectangleLebesgue IntegralThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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