Chapter 48: Gauge integrals
481
Tagged partitions
Tagged partitions and Riemann sums; gauge integrals; gauges;
residual sets; subdivisions; examples (the Riemann integral, the
Henstock integral, the symmetric Riemann-complete integral, the
McShane integral, box products, the approximately continuous Henstock
integral).
482
General theory
Saks-Henstock lemma; when gauge-integrable functions are
measurable; when integrable functions are gauge-integrable;
Iν(f×χH); improper integrals; integrating
derivatives; B.Levi's theorem; Fubini's theorem.
483
The Henstock integral
The Henstock and Lebesgue integrals; indefinite Henstock integrals;
Saks-Henstock lemma; Fundamental Theorem of Calculus; the Perron
integral; ∥f∥H and HL1; AC* and ACG* functions.
484
The Pfeffer integral
The Tamanini-Giacomelli theorem; a family of tagged-partition
structures; the Pfeffer integral; the Saks-Henstock indefinite
integral of a Pfeffer integrable function; Pfeffer's Divergence
Theorem; differentiating the indefinite integral; invariance under
lipeomorphisms.
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