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Erschienen in:
1999 | OriginalPaper | Buchkapitel
Lebesgue Integral
verfasst von : Sterling K. Berberian
Erschienen in: Fundamentals of Real Analysis
Verlag: Springer New York
Enthalten in: Professional Book Archive
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Chapter 2 lays the foundation for the Lebesgue integral. What comes first is the concept of outer measure, a natural extension of interval length; the class of measurable sets is then defined in terms of the outer measure, guided by the need for additivity of measure as a set function. Outer measure provides the raw numbers; measurability provides the ‘smooth’ sets on which the numbers are well-behaved. Such well-behavior is codified in the concept of measure space.