0. Introduction -- 1. Integrable functions and their primitives -- 2. Gauges and Borel measurability -- 3. Convergence -- 4. An abstract setting -- 5. An abstract setting with D countable -- 6. Locally convex topologies tolerant to Q-convergence -- 7. Topological vector spaces t…
Henstock-Kurzweil (HK) integration, which is based on integral sums, can be obtained by an inconspicuous change in the definition of Riemann integration. It is an extension of Lebesgue integration and there exists an HK-integrable function f such that its absolute value.
0. Introduction -- 1. Basic concepts and properties of [symbol]-integration -- 2. Convergence -- 3. Convergence and locally convex spaces -- 4. An auxiliary locally convex space -- 5. [symbol]-integration -- 6. M-integration -- 7. Noncompleteness -- 8. S-integration -- 9. R-inte…
The main topics of this book are convergence and topologization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Den…
This paper deals with the integration of abstract Henstock type. Eleven derivation bases on the plane are investigated, those built with triangles, rectangles, and regular rectangles, and the approximate bases. The relationships between the integration theories generated by them…
Ce Petit traité d'intégration développe une approche originale de l'intégrale. Cette approche, que l'on pourrait qualifier de globale, est due aux deux mathématiciens Jaroslaw Kurzweil et Ralph Henstock. L'enseignement de l'intégration se fait d'ordinaire en deux temps. On début…
Stochastic integration -- Random variation -- Integration and probability -- Stochastic processes -- Brownian motion -- Stochastic sums -- Gauges for product spaces -- Quantum field theory -- Quantum electrodynamics.