Integration between the Lebesgue integral and the Henstock-Kurzweil integral : its relation to local convex vector spaces /

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 th...

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Bibliographic Details
Main Author: Kurzweil, Jaroslav.
Format: eBook
Language:English
Published: Singapore ; River Edge, N.J. : World Scientific, ©2002.
Series:Series in real analysis ; v. 8.
Subjects:
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245 1 0 |a Integration between the Lebesgue integral and the Henstock-Kurzweil integral :  |b its relation to local convex vector spaces /  |c Jaroslav Kurzweil. 
260 |a Singapore ;  |a River Edge, N.J. :  |b World Scientific,  |c ©2002. 
300 |a 1 online resource (vii, 140 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 1 |a Series in real analysis ;  |v v. 8 
504 |a Includes bibliographical references (page 135) and indexes. 
588 0 |a Print version record. 
505 0 |a Preface; CONTENTS; 0. Introduction; 1. Basic concepts and properties of y-integration; 1.1 Notation.; 1.2 Lemma (Cousin).; 1.3 Definition.; 1.4 Theorem.; 1.5 Definition.; 1.6 Theorem.; 1.7 Lemma (Saks Henstock).; 1.8 Definition.; 1.9 Theorem.; 1.10 Note.; 1.11 Definition.; 1.12 Theorem.; 1.13 Lemma.; 1.14 Theorem.; 1.15 Lemma.; 1.16 Theorem.; 2. Convergence; 2.1. Theorem.; 2.2 Definition.; 2.3 Lemma.; 2.4 Lemma.; 2.5 Lemma.; 2.6 Definition.; 2.7 Lemma.; 2.8 Lemma.; 2.9 Theorem.; 2.10 Theorem.; 2.11 Definition.; 2.12 Theorem.; 2.13 Lemma.; 2.14 Definition.; 2.15 Lemma.; 2.16 Theorem. 
505 8 |a 3. Convergence and locally convex spaces3.1 Preliminaries.; 3.2 Lemma.; 3.3 Definition.; 3.4 Notation.; 3.5 Lemma.; 3.6 Note.; 3.7 Theorem.; 3.8 Lemma.; 3.9 Theorem.; 3.10 Lemma.; 3.11 Lemma.; 3.12 Lemma.; 3.13 Lemma.; 3.14 Theorem; 3.15 Lemma.; 4. An auxiliary locally convex space; 4.1 Preliminaries.; 4.2 Theorem.; 4.3 Lemma.; 4.4 Lemma.; 4.5 Lemma.; 4.6 Notation.; 4.7 Lemma.; 4.8 Theorem.; 5. L-integration; 5.1 Preliminaries.; 5.2 Theorem.; 5.3 Theorem.; 5.4 Lemma.; 5.5 Lemma.; 5.6 Lemma.; 5.7 Lemma.; 5.8 Example.; 5.9 Theorem.; 5.10 Remark.; 5.11 Remark.; 5.12 Theorem.; 6. .M-integration. 
505 8 |a 6.1 Notation. 6.2 Definition.; 6.3 Theorem.; 6.4 Definition.; 6.5 Lemma.; 6.6.; 6.7 Lemma.; 6.8 Lemma.; 6.9 Lemma.; 6.10 Lemma.; 6.11 Lemma.; 6.12 Lemma.; 7. Noncompleteness; 7.1 A restriction on y.; 7.2 Lemma.; 7.3 Theorem.; 7.4 Lemma.; 7.5 Notation and some observations.; 7.6 Lemma.; 7.7 Lemma.; 7.8 Lemma.; 7.9 Lemma.; 7.10 Theorem.; 8. S-integration; 8.1 Preliminaries.; 8.2 Theorem.; 8.3 Theorem.; 8.4 Lemma.; 8.5 Lemma.; 8.6 Lemma.; 8.7 Lemma.; 8.8 Remark .; 8.9 Theorem.; 8.10 Theorem.; 8.11 Theorem.; 8.12 Lemma.; 9. R-integration; 9.1 Preliminaries.; 9.2 Theorem.; 9.3 Notation.; 9.4 Lemma. 
505 8 |a 9.5 Note. 10. An extension of the concept of y-integration; 10.1 Introduction.; 10.2 Definition.; 10.3 Definition.; 10.4 X(S*)-integration.; 10.5 Remark.; 10.6 X(R*)-integration.; 11. Differentiation and integration; 11.1 Definition.; 11.2 Definition.; 11.3 Theorem.; 11.4 Theorem.; 11.5 Remarks.; 11.6 Notation.; 11.7 Theorem.; 11.8 Theorem.; 11.9 Theorem.; 11.10 Theorem.; 11.11 Lemma.; 11.12 Theorem.; 11.13 Theorem.; 11.14 Remark.; 11.15 Remark.; 11.16 Theorem.; References; List of symbols; Index. 
520 |a 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 student. 
546 |a English. 
590 |a EBSCO eBook Academic Comprehensive Collection North America 
650 0 |a Lebesgue integral. 
650 0 |a Henstock-Kurzweil integral. 
650 0 |a Vector spaces. 
730 0 |a WORLDSHARE SUB RECORDS 
776 0 8 |i Print version:  |a Kurzweil, Jaroslav.  |t Integration between the Lebesgue integral and the Henstock-Kurzweil integral.  |d Singapore ; River Edge, N.J. : World Scientific, ©2002  |z 9812380469  |w (OCoLC)50530128 
830 0 |a Series in real analysis ;  |v v. 8. 
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