Lanzhou Lectures on Henstock IntegrationWorld Scientific, 1989 - 179 Seiten This is an introductory book on Henstock integration, otherwise known as generalized Riemann integral. It is self-contained and introductory. The author has included a series of convergence theorems for the integral, previously not available. In this book, he has also developed a technique of proof required to present the new as well as the classical results. |
Inhalt
THE DENJOYPERRON INTEGRAL | 27 |
8 | 36 |
9 | 45 |
RIESZ REPRESENTATION THEOREMS | 66 |
13 | 81 |
Orthogonally additive functionals on the Denjoy space | 95 |
THE RIEMANNTYPE INTEGRALS | 104 |
Locally small Riemann sums | 110 |
19 | 118 |
SOME GENERALIZATIONS | 127 |
Approximately continuous integrals | 136 |
The CesaroPerron integral | 145 |
The Kunugi integral | 160 |
| 171 | |
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8-fine division absolutely Henstock integrable AP integrable bounded variation closed sets continuous function continuous on a,b control-convergent to f controlled convergence theorem convergence theorem Theorem convergent to f Corollary D₁ D₂ defined Definition Denjoy integrable Denjoy space denote DL integrable dominated convergence theorem E₁ endpoints everywhere in a,b Example exists f is absolutely F is AC f is Henstock F is VBG F of f f on a,b function f functions on a,b G₁ given Henstock integrable function inequality integrable on a,b integral of f Lebesgue integral Let f McShane integrable measurable function minor functions monotone convergence theorem non-negative open set orthogonally additive partial division Perron integrable primitive F primitive of f proof is complete proof of Theorem prove Riemann integrable Riemann sum Sargent space sequence of non-overlapping step functions subinterval Suppose f supremum Theorem 7.1 variation on a,b X₁ Y₁
Verweise auf dieses Buch
The Integrals of Lebesgue, Denjoy, Perron, and Henstock Russell A. Gordon Eingeschränkte Leseprobe - 1994 |
The Space of Mathematics: Philosophical, Epistemological, and Historical ... Javier Echeverría,Andoni Ibarra,Thomas Mormann Eingeschränkte Leseprobe - 1992 |