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from PART I - Measure And Integration
Published online by Cambridge University Press: 06 January 2022
This chapter starts with definitions and basic properties of Measurable Functions. The Lebesgue Integral is systematically developed; first for Simple Functions, then for Nonnegative Functions, and finally for the General Case. Egorov's Theorem is proven. The important Lebesgue Limit Theorems that distinguish Lebesgue Integration from Riemann and Stieltjes Integration are discussed and proven.
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