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