Integration Between the Lebesgue Integral and the Henstock-Kurzweil Integral: Its Relation to Local Convex Vector Spaces

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Juni 2002



The main topics of this book are convergence and topoligization. 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 Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear.The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by students, since only the basics of mathematical analysis and vector spaces are required.


Contents: Basic Concepts and Properties of y-Integration; Convergence; Convergence and Locally Convex Spaces; An Auxiliary Locally Convex Space; L-Integration; M-Integration; Noncompleteness; S-Integration; R-Integration; An Extension of the Concept of y-Integration; Differentiation and Integration.


Jaroslav Kurzweil is a professor at the Mathematical Institute of the Academy of Sciences of the Czech Republic. He is also the author of the other five books and has published 105 original papers. He is now retired but remained the Chairman of the Accreditation Commission of the institute and Chairman of the Union of Czech Mathematicians and Physicists. He was elected as the Honorary Foreign Fellow of the Royal Society of Edinburgh in 1978 and Corresponding Member of the Academie Royale de Belgique, Classe des Sciences.

EAN: 9789812380463
ISBN: 9812380469
Untertitel: 'Series in Real Analysis'. Sprache: Englisch.
Erscheinungsdatum: Juni 2002
Seitenanzahl: 140 Seiten
Format: gebunden
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