ABSTRACT
Lebesgue Measure In Chapter 11 we shall present a theory of integration more general than the Riemann theory of Chapter 8, called Lebesgue integration, which is due to the French mathematician Henri Lebesgue (1875-1941). From among the standard approaches to this theory, we shall follow the path based on first extending the notion of length of a real interval to define the so-called Lebesgue measure of certain subsets of R, which forms the subject of this chapter, then using this to define the Lebesgue integral in Chapter 11. This approach has the advantage of giving prominence to measure as a fundamental mathematical concept in its own right with wide applications in probability and stochastic theory, besides providing the cornerstone for building a more complete integration theory, in a sense which will be clarified in the next chapter.
