Contents of Measure Theory, by D.H.Fremlin

Chapter 12: Integration

121 Measurable functions
Subspace s-algebras; measurable real-valued functions; partially defined functions; Borel measurable functions; operations on measurable functions; generating Borel sets from half-spaces.

122 Definition of the integral
Simple functions; non-negative integrable functions; integrable real-valued functions; virtually measurable functions; linearity of the integral.

123 The convergence theorems
B.Levi's theorem; Fatou's lemma; Lebesgue's Dominated Convergence Theorem; differentiating through an integral.

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Revised 10.4.05