Lectures on the theory of integration:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1988
|
| Series: | Series in real analysis
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 206 S. |
| ISBN: | 9971504502 9971504510 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV002068336 | ||
| 003 | DE-604 | ||
| 005 | 20000403 | ||
| 007 | t | ||
| 008 | 890928s1988 |||| 00||| eng d | ||
| 020 | |a 9971504502 |9 9971-50-450-2 | ||
| 020 | |a 9971504510 |9 9971-50-451-0 | ||
| 035 | |a (OCoLC)18277134 | ||
| 035 | |a (DE-599)BVBBV002068336 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91 |a DE-739 |a DE-824 |a DE-703 |a DE-19 |a DE-706 |a DE-11 | ||
| 050 | 0 | |a QA312 | |
| 082 | 0 | |a 517.1 | |
| 084 | |a SK 430 |0 (DE-625)143239: |2 rvk | ||
| 084 | |a MAT 280f |2 stub | ||
| 100 | 1 | |a Henstock, Ralph |d 1923-2007 |e Verfasser |0 (DE-588)118911406 |4 aut | |
| 245 | 1 | 0 | |a Lectures on the theory of integration |c Ralph Henstock |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1988 | |
| 300 | |a XII, 206 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series in real analysis |v 1 | |
| 650 | 4 | |a Integrals, Generalized | |
| 650 | 4 | |a Integration, Functional | |
| 650 | 4 | |a Measure theory | |
| 650 | 0 | 7 | |a Integrationstheorie |0 (DE-588)4138369-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Integrationstheorie |0 (DE-588)4138369-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Series in real analysis |v 1 |w (DE-604)BV001898092 |9 1 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001352751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001352751 | ||
Record in the Search Index
| _version_ | 1804116518674366464 |
|---|---|
| adam_text | CONTENTS
Preface (vii)
0 Prerequisites (ix)
CHAPTER 1 INTRODUCTION 1
1 The Riemann and Riemann Darboux integrals 1
2 Modifications using the mesh and refinement of partitions 4
3 The calculus indefinite integral and the Riemann complete or
generalized Riemann integral 29
CHAPTER 2 SIMPLE PROPERTIES OF THE GENERALIZED RIEMANN INTEGRAL
IN FINITE DIMENSIONAL EUCLIDEAN SPACE 41
4 Integration over a fixed elementary set 41
5 Integration and variation over more than one elementary set 51
6 The integrability of functions of brick point functions 75
7 The variation set 83
CHAPTER 3 LIMIT THEOREMS FOR SEQUENCES OF FUNCTIONS 90
8 Monotone convergence 90
9 Bounded Riemann sums and the majorized (dominated) convergence
test 95
10 Controlled convergence 102
11 Necessary and sufficient conditions 105
12 Mean convergence and l spaces 108
CHAPTER 4 LIMIT THEOREMS FOR MORE GENERAL CONVERGENCE, WITH
CONTINUITY 123
13 Basic theorems 123
14 Fatou s lemma and the avoidance of nonmeasurable functions 129
CHAPTER 5 DIFFERENTIATION, MEASURABILITY, AND INNER VARIATION 133
15 Differentiation of integrals 133
16 Limits of step functions 149
CHAPTER 6 CARTESIAN PRODUCTS AND THE FUBINI AND TONELLI THEOREMS 162
17 Fubini type theorems 162
18 Tonelli type theorems and the necessary and sufficient
condition for reversal of order of double integrals 169
v
CHAPTER 7 APPLICATIONS 176
19 Ordinary differential equations 176
20 Statistics and probability theory 180
CHAPTER 8 HISTORY AND FURTHER DISCUSSION
21 Other integrals 191
22 Notes on the previous sections 196
REFERENCES 199
INDEX 204
vi
|
| any_adam_object | 1 |
| author | Henstock, Ralph 1923-2007 |
| author_GND | (DE-588)118911406 |
| author_facet | Henstock, Ralph 1923-2007 |
| author_role | aut |
| author_sort | Henstock, Ralph 1923-2007 |
| author_variant | r h rh |
| building | Verbundindex |
| bvnumber | BV002068336 |
| callnumber-first | Q - Science |
| callnumber-label | QA312 |
| callnumber-raw | QA312 |
| callnumber-search | QA312 |
| callnumber-sort | QA 3312 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 430 |
| classification_tum | MAT 280f |
| ctrlnum | (OCoLC)18277134 (DE-599)BVBBV002068336 |
| dewey-full | 517.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.1 |
| dewey-search | 517.1 |
| dewey-sort | 3517.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01557nam a2200421 cb4500</leader><controlfield tag="001">BV002068336</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20000403 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1988 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9971504502</subfield><subfield code="9">9971-50-450-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9971504510</subfield><subfield code="9">9971-50-451-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)18277134</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002068336</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA312</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">517.1</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 430</subfield><subfield code="0">(DE-625)143239:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 280f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Henstock, Ralph</subfield><subfield code="d">1923-2007</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)118911406</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lectures on the theory of integration</subfield><subfield code="c">Ralph Henstock</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore [u.a.]</subfield><subfield code="b">World Scientific</subfield><subfield code="c">1988</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 206 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Series in real analysis</subfield><subfield code="v">1</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integrals, Generalized</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integration, Functional</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Measure theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integrationstheorie</subfield><subfield code="0">(DE-588)4138369-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Integrationstheorie</subfield><subfield code="0">(DE-588)4138369-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Series in real analysis</subfield><subfield code="v">1</subfield><subfield code="w">(DE-604)BV001898092</subfield><subfield code="9">1</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001352751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001352751</subfield></datafield></record></collection> |
| id | DE-604.BV002068336 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:39:47Z |
| institution | BVB |
| isbn | 9971504502 9971504510 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001352751 |
| oclc_num | 18277134 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-739 DE-824 DE-703 DE-19 DE-BY-UBM DE-706 DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-739 DE-824 DE-703 DE-19 DE-BY-UBM DE-706 DE-11 |
| physical | XII, 206 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in real analysis |
| series2 | Series in real analysis |
| spelling | Henstock, Ralph 1923-2007 Verfasser (DE-588)118911406 aut Lectures on the theory of integration Ralph Henstock Singapore [u.a.] World Scientific 1988 XII, 206 S. txt rdacontent n rdamedia nc rdacarrier Series in real analysis 1 Integrals, Generalized Integration, Functional Measure theory Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s DE-604 Series in real analysis 1 (DE-604)BV001898092 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001352751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Henstock, Ralph 1923-2007 Lectures on the theory of integration Series in real analysis Integrals, Generalized Integration, Functional Measure theory Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4138369-2 |
| title | Lectures on the theory of integration |
| title_auth | Lectures on the theory of integration |
| title_exact_search | Lectures on the theory of integration |
| title_full | Lectures on the theory of integration Ralph Henstock |
| title_fullStr | Lectures on the theory of integration Ralph Henstock |
| title_full_unstemmed | Lectures on the theory of integration Ralph Henstock |
| title_short | Lectures on the theory of integration |
| title_sort | lectures on the theory of integration |
| topic | Integrals, Generalized Integration, Functional Measure theory Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Integrals, Generalized Integration, Functional Measure theory Integrationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001352751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001898092 |
| work_keys_str_mv | AT henstockralph lecturesonthetheoryofintegration |