Contents of Measure Theory, by D.H.Fremlin

Chapter 13: Complements

131 Measurable subspaces
Subspace measures on measurable subsets; integration over measurable subsets.

132 Outer measures from measures
The outer measure associated with a measure; Lebesgue outer measure again; measurable envelopes.

133 Wider concepts of integration
∞ as a value of an integral; complex-valued functions; upper and lower integrals.

134 More on Lebesgue measure
Translation-invariance; non-measurable sets; inner and outer regularity; the Cantor set and function; *the Riemann integral.

135 The extended real line
The algebra of ±∞; Borel sets and convergent sequences in [-∞,∞]; measurable and integrable [-∞,∞]-valued functions.

*136 The Monotone Class Theorem
The σ-algebra generated by a family I; algebras of sets.

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Revised 11.6.2016