Chapter 13: Complements
Subspace measures on measurable subsets; integration over measurable subsets.
Outer measures from measures
The outer measure associated with a measure; Lebesgue outer measure again; measurable envelopes.
Wider concepts of integration
∞ as a value of an integral; complex-valued functions; upper and lower integrals.
More on Lebesgue measure
Translation-invariance; non-measurable sets; inner and outer regularity; the Cantor set and function; *the Riemann integral.
The extended real line
The algebra of ±∞; Borel sets and convergent sequences in [-∞,∞]; measurable and integrable [-∞,∞]-valued functions.
The Monotone Class Theorem
The σ-algebra generated by a family I; algebras of sets.
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