A Modern View of the Riemann Integral / Lecture Notes in Mathematics Bd.2309 (PDF)
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This approach rests on three basic observations. First, a Riemann integrability criterion in terms of oscillations, which is a quantitative formulation of the fact that Riemann integrable functions are continuous a.e. with respect to the Lebesgue measure. Second, the introduction of the concepts of admissible families of partitions and modified Riemann sums. Finally, the fact that most numerical quadrature rules make use of carefully chosen Riemann sums, which makes the Riemann integral, be it proper or improper, most appropriate for this endeavor.
A Modern View of the Riemann Integral is intended for enthusiasts keen to explorethe potential of Riemann's original notion of integral. The only formal prerequisite is a proof-based familiarity with the Riemann integral, though readers will also need to draw upon mathematical maturity and a scholarly outlook.
- Autor: Alberto Torchinsky
- 2022, 1st ed. 2022, 176 Seiten, Englisch
- Verlag: Springer International Publishing
- ISBN-10: 3031117999
- ISBN-13: 9783031117992
- Erscheinungsdatum: 05.10.2022
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