Chapter 12: Integration
Subspace s-algebras; measurable real-valued functions; partially defined functions; Borel measurable functions; operations on measurable functions; generating Borel sets from half-spaces.
Definition of the integral
Simple functions; non-negative integrable functions; integrable real-valued functions; virtually measurable functions; linearity of the integral.
The convergence theorems
B.Levi's theorem; Fatou's lemma; Lebesgue's Dominated Convergence Theorem; differentiating through an integral.
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