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