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El. knyga: Integration Between The Lebesgue Integral And The Henstock-kurzweil Integral: Its Relation To Local Convex Vector Spaces

(Academy Of Sciences, Czech Republic)
  • Formatas: 148 pages
  • Serija: Series In Real Analysis 8
  • Išleidimo metai: 14-Jun-2002
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789814488266
Kitos knygos pagal šią temą:
Integration Between The Lebesgue Integral And The Henstock-kurzweil Integral: Its Relation To Local Convex Vector SpacesDidesnis paveikslėlis
  • Formatas: 148 pages
  • Serija: Series In Real Analysis 8
  • Išleidimo metai: 14-Jun-2002
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789814488266
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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 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.
Preface v
Introduction
1(8)
Basic concepts and properties of Y-integration
9(12)
Convergence
21(11)
Convergence and locally convex spaces
32(10)
An auxiliary locally convex space
42(10)
L-integration
52(17)
M-integration
69(7)
Noncompleteness
76(10)
S-integration
86(18)
R-integration
104(5)
An extension of the concept of Y-integration
109(7)
Differentiation and integration
116(19)
References 135(2)
List of symbols 137(2)
Index 139


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.
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