The integrals of Lebesgue, Denjoy, Perron, and Henstock

Russell A. Gordon.

Providence, R.I. : American Mathematical Society, ©1994.

xi, 395 págs. ; 27 cm.

Serie: Graduate studies in mathematics, ISSN 1065-7339 ; v. 4

ISBN: 0821838059

Resumen: Suppose that f : [a,b] -> R is differentiable at each point of [a,b]. Is f' integrable on [a,b]? The answer to this question depends on the integral that is used. For example, the answer is no for the Riemann and Lebesgue integrals. In this century, three integrations processes have been developed that provide an affirmative answer to this question. The principal investigators of these integrals were Denjoy, Perron, and Henstock. Each of these integrals generalizes a different property of the Lebesgue integral, but it turns out that all three integrals are equivalent. In this book, the properties of the Lebesgue, Denjoy, Perron, and Henstock integrals are developed fully from their definitions. The equivalence of the last three integrals is then established. Discussions of the integration by parts formula and convergence theorems are included. In the last part of the book, we consider approximate derivatives and attempts to develop an integration process for which every approximate derivative is integrable.

Incluye referencias bibliográficas (p. 389-390) e índices.

Reseña: MathSciNet, 95m:26010