Integration theory: a second course
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2002
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010047603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VIII, 277 S. |
| ISBN: | 9812381155 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV014855442 | ||
| 003 | DE-604 | ||
| 005 | 20080425 | ||
| 007 | t| | ||
| 008 | 021106s2002 xx |||| 00||| eng d | ||
| 020 | |a 9812381155 |9 981-238-115-5 | ||
| 035 | |a (OCoLC)249518388 | ||
| 035 | |a (DE-599)BVBBV014855442 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-20 |a DE-355 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA312 | |
| 082 | 0 | |a 515.42 | |
| 084 | |a SK 430 |0 (DE-625)143239: |2 rvk | ||
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Väth, Martin |d 1967- |e Verfasser |0 (DE-588)115361499 |4 aut | |
| 245 | 1 | 0 | |a Integration theory |b a second course |c Martin Väth |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2002 | |
| 300 | |a VIII, 277 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Integrationstheorie | |
| 650 | 0 | 7 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |2 gnd |9 rswk-swf |
| 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 | |
| 689 | 1 | 0 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010047603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010047603 | |
Datensatz im Suchindex
| _version_ | 1819306536934047744 |
|---|---|
| adam_text | Contents
Preface
v
Part
1:
Basic
Integration Theory
1
Overview
3
1.
Abstract Integration
5
1.1
Basic Notions
.......................... 5
1.2
Measurable Functions
..................... 10
1.3
Definition of the Integral and Convergence Theorems
.... 38
1.4
Extension of Measures
..................... 64
1.5
Product Measures and Fubini s Theorem
........... 75
1.6
Exercises
............................ 89
2.
Adding a Topological Structure: The Radon Measure
95
2.1
Preliminaries from Topology
.................. 95
2.2
Borei
Measures and Luzin s Theorem
............. 108
2.3
Radon Measures
........................ 113
2.4
Exercises
............................ 125
3.
Adding a Group Structure: The
Haar
Measure
129
3.1
Preliminaries from Topological Groups
............ 129
3.2
The
Haar
Measure
....................... 132
3.3
Exercises
............................ 149
vii
viii Contents
Part
2:
Advanced Topics
151
4.
Spaces of Measurable Functions
153
4.1
Lp Spaces
............................ 153
4.2
Ideal Spaces
........................... 156
4.3
Dual Spaces
........................... 167
4.4
Exercises
............................ 178
5.
Convolutions
183
5.1
The Modular Function
..................... 183
5.2
Convolutions
.......................... 190
5.3
Exercises
............................ 198
6.
Connections with Logic and Set Theory
201
6.1
The Axiom of Choice and the Continuum Hypothesis
.... 201
6.2
The Banach-Tarski Paradox
.................. 213
6.3
Consequences on Measure Theory
............... 217
6.4
Exercises
............................ 229
7.
Special Properties of the Lebesgue Measure
233
7.1
Connections with the Riemann Integral
........... 233
7.2
The Fundamental Theorem of Calculus
............ 237
7.3
Exercises
............................ 247
8.
Miscellaneous
249
8.1
Some Useful Formulas
..................... 249
8.2
The Graph of a Function and Rearrangements
....... 255
8.3
Exercises
............................ 263
Bibliography
265
Index
269
|
| any_adam_object | 1 |
| author | Väth, Martin 1967- |
| author_GND | (DE-588)115361499 |
| author_facet | Väth, Martin 1967- |
| author_role | aut |
| author_sort | Väth, Martin 1967- |
| author_variant | m v mv |
| building | Verbundindex |
| bvnumber | BV014855442 |
| 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 |
| ctrlnum | (OCoLC)249518388 (DE-599)BVBBV014855442 |
| dewey-full | 515.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 |
| dewey-search | 515.42 |
| dewey-sort | 3515.42 |
| 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>01476nam a2200397 c 4500</leader><controlfield tag="001">BV014855442</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080425 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">021106s2002 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812381155</subfield><subfield code="9">981-238-115-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)249518388</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014855442</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA312</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.42</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">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Väth, Martin</subfield><subfield code="d">1967-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)115361499</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integration theory</subfield><subfield code="b">a second course</subfield><subfield code="c">Martin Väth</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New Jersey [u.a.]</subfield><subfield code="b">World Scientific</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 277 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="650" ind1=" " ind2="4"><subfield code="a">Integrationstheorie</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integration</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4072852-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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="689" ind1="1" ind2="0"><subfield code="a">Integration</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4072852-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</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=010047603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-010047603</subfield></datafield></record></collection> |
| id | DE-604.BV014855442 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:08:56Z |
| institution | BVB |
| isbn | 9812381155 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010047603 |
| oclc_num | 249518388 |
| open_access_boolean | |
| owner | DE-824 DE-20 DE-355 DE-BY-UBR DE-11 DE-188 |
| owner_facet | DE-824 DE-20 DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | VIII, 277 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific |
| record_format | marc |
| spellingShingle | Väth, Martin 1967- Integration theory a second course Integrationstheorie Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4072852-3 (DE-588)4138369-2 |
| title | Integration theory a second course |
| title_auth | Integration theory a second course |
| title_exact_search | Integration theory a second course |
| title_full | Integration theory a second course Martin Väth |
| title_fullStr | Integration theory a second course Martin Väth |
| title_full_unstemmed | Integration theory a second course Martin Väth |
| title_short | Integration theory |
| title_sort | integration theory a second course |
| title_sub | a second course |
| topic | Integrationstheorie Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Integrationstheorie Integration Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010047603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT vathmartin integrationtheoryasecondcourse |