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...
Saved in:
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Singapore ; River Edge, N.J. :
World Scientific,
©2002.
|
| Series: | Series in real analysis ;
v. 8. |
| Subjects: | |
| Online Access: | CONNECT CONNECT |
| LEADER | 05690cam a2200661Ka 4500 | ||
|---|---|---|---|
| 001 | mig00005324767 | ||
| 003 | OCoLC | ||
| 005 | 20210517055544.4 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 130222s2002 si ob 001 0 eng d | ||
| 010 | |z 2002512064 | ||
| 019 | |a 666957658 |a 854973968 |a 1162419028 |a 1241786203 | ||
| 020 | |a 9789812777195 |q (electronic bk.) | ||
| 020 | |a 9812777199 |q (electronic bk.) | ||
| 020 | |z 9812380469 | ||
| 020 | |z 9789812380463 | ||
| 020 | |a 1281929549 | ||
| 020 | |a 9781281929549 | ||
| 020 | |a 9786611929541 | ||
| 020 | |a 6611929541 | ||
| 035 | |a (OCoLC)828180165 |z (OCoLC)666957658 |z (OCoLC)854973968 |z (OCoLC)1162419028 |z (OCoLC)1241786203 | ||
| 035 | 0 | 0 | |a ocm00000001wrldshrocn828180165 |
| 040 | |a N$T |b eng |e pn |c N$T |d IDEBK |d OCLCF |d EBLCP |d DEBSZ |d OCLCQ |d YDXCP |d OCLCQ |d AGLDB |d OCLCQ |d OCLCO |d JBG |d VTS |d REC |d OCLCO |d LEAUB |d OCLCO |d AU@ |d OCLCO |d M8D |d UKAHL |d OCLCQ |d K6U |d VLY | ||
| 049 | |a TXMM | ||
| 050 | 4 | |a QA312 K87 2002 | |
| 082 | 0 | 4 | |a 515/.43 |2 22 |
| 084 | |a SK 430 |2 rvk | ||
| 100 | 1 | |a Kurzweil, Jaroslav. | |
| 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 | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 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. | |
| 856 | 4 | 0 | |u https://ezproxy.mtsu.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=514323 |z CONNECT |3 EBSCO |
| 907 | |a 4595346 |b 05-25-21 |c 06-30-20 | ||
| 998 | |a wi |b 05-25-21 |c m |d z |e - |f eng |g si |h 0 |i 2 | ||
| 994 | |a 92 |b TXM | ||
| 999 | f | f | |i 2857b7ad-c574-4266-9da5-29e2605903a8 |s 7df7b260-2d9a-4328-801c-5334ce8383fa |
| 952 | f | f | |e QA312 K87 2002 |h Library of Congress classification |
| 856 | 4 | 0 | |3 EBSCO |u https://ezproxy.mtsu.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=514323 |z CONNECT |
