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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