Contents of Measure Theory, by D.H.Fremlin

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; ∥fH 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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Revised 17.5.11