Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration

Igor Kriz and Aleš Pultr
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Igor Kriz: University of Michigan, Department of Mathematics
Aleš Pultr: Charles University, Department of Applied Mathematics (KAM) Faculty of Mathematics and Physics

Chapter 5 in Introduction to Mathematical Analysis, 2013, pp 117-143 from Springer

Abstract: Abstract (Lebesgue’s Monotone Convergence Theorem) Let $$f_{n} \in { \mathfrak{L}}^{\mathsf{up}}$$ and let $$f_{n} \nearrow f$$ a.e. Then $$f \in {\mathfrak{L}}^{\mathsf{up}}$$ and ∫f = lim ∫f n . Similarly for $$f_{n} \in {\mathfrak{L}}^{\mathsf{dn}}$$ and f n ↘ f.

Date: 2013
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DOI: 10.1007/978-3-0348-0636-7_5

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