Integration - a functional approach:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1998
|
| Series: | Birkhäuser advanced texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 193 S. |
| ISBN: | 3764359366 0817659366 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV011849152 | ||
| 003 | DE-604 | ||
| 005 | 20010920 | ||
| 007 | t | ||
| 008 | 980317s1998 gw |||| 00||| eng d | ||
| 016 | 7 | |a 953180531 |2 DE-101 | |
| 020 | |a 3764359366 |9 3-7643-5936-6 | ||
| 020 | |a 0817659366 |9 0-8176-5936-6 | ||
| 035 | |a (OCoLC)38910271 | ||
| 035 | |a (DE-599)BVBBV011849152 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-384 |a DE-20 |a DE-739 |a DE-29T |a DE-824 |a DE-898 |a DE-355 |a DE-91G |a DE-19 |a DE-521 |a DE-526 |a DE-634 |a DE-188 | ||
| 050 | 0 | |a QA312.B53 1998 | |
| 082 | 0 | |a 515/.43 21 | |
| 082 | 0 | |a 515/.43 |2 21 | |
| 084 | |a SK 430 |0 (DE-625)143239: |2 rvk | ||
| 084 | |a 27 |2 sdnb | ||
| 084 | |a MAT 280f |2 stub | ||
| 100 | 1 | |a Bichteler, Klaus |d 1938- |e Verfasser |0 (DE-588)106060279 |4 aut | |
| 245 | 1 | 0 | |a Integration - a functional approach |c Klaus Bichteler |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1998 | |
| 300 | |a VIII, 193 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Birkhäuser advanced texts | |
| 650 | 4 | |a Integrals | |
| 650 | 4 | |a Measure theory | |
| 650 | 0 | 7 | |a Integrationstheorie |0 (DE-588)4138369-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maßtheorie |0 (DE-588)4074626-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lebesgue-Integral |0 (DE-588)4034949-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemannsches Integral |0 (DE-588)4049996-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Integrationstheorie |0 (DE-588)4138369-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Maßtheorie |0 (DE-588)4074626-4 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Riemannsches Integral |0 (DE-588)4049996-0 |D s |
| 689 | 3 | |8 1\p |5 DE-604 | |
| 689 | 4 | 0 | |a Lebesgue-Integral |0 (DE-588)4034949-4 |D s |
| 689 | 4 | |8 2\p |5 DE-604 | |
| 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=008003466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008003466 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804126434462007297 |
|---|---|
| adam_text | Contents
Preface vii
Chapter I Review 1
1.1 Introduction 1
1.2 Notation 3
1.3 The Theorem of Stone Weierstrafi 8
1.4 The Riemann Integral 17
1.5 An Integrability Criterion 21
1.6 The Permanence Properties 23
1.7 Seminorms 28
Chapter II Extension of the Integral 31
II. 1 E additivity 33
11.2 Elementary Integrals 35
11.3 The Daniell Mean 42
11.4 Negligible Functions and Sets 48
11.5 Integrable Functions 52
11.6 Extending the Integral 58
11.7 Integrable Sets 61
11.8 Example of a Non Integrable Function 66
Chapter III Measurability 69
111.1 Littlewood s Principles 70
111.2 The Permanence Properties 73
111.3 The Integrability Criterion 75
111.4 Measurable Sets 81
111.5 Baire and Borel Functions 85
111.6 Further Properties of Daniell s Mean 92
111.7 The Procedures of Lebesgue and Carathedory 95
vi
Chapter IV The Classical Banach Spaces 101
IV.1 The p norms 102
IV.2 The CP spaces 105
IV.3 The LP spaces 108
IV.4 Linear Functionals 112
IV.5 The Dual of LP 118
IV.6 The Hilbert space L2 122
Chapter V Operations on Measures 125
V.I Products of Elementary Integrals 125
V.2 The Theorems of Fubini and Tonelli 130
V.3 An Application: Convolution 133
V.4 An Application: Marcinkiewicz Interpolation 134
V.5 Signed Measures 137
V.6 The Space of Measures 144
V.7 Measures with Densitites 151
V.8 The Radon Nikodym Theorem 154
V.9 An Application: Conditional Expectation 155
V.10 Differentiation 157
Appendix A Answers to Selected Problems 165
References 180
Index of Notations 181
Index 184
|
| any_adam_object | 1 |
| author | Bichteler, Klaus 1938- |
| author_GND | (DE-588)106060279 |
| author_facet | Bichteler, Klaus 1938- |
| author_role | aut |
| author_sort | Bichteler, Klaus 1938- |
| author_variant | k b kb |
| building | Verbundindex |
| bvnumber | BV011849152 |
| callnumber-first | Q - Science |
| callnumber-label | QA312 |
| callnumber-raw | QA312.B53 1998 |
| callnumber-search | QA312.B53 1998 |
| callnumber-sort | QA 3312 B53 41998 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 430 |
| classification_tum | MAT 280f |
| ctrlnum | (OCoLC)38910271 (DE-599)BVBBV011849152 |
| dewey-full | 515/.4321 515/.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.43 21 515/.43 |
| dewey-search | 515/.43 21 515/.43 |
| dewey-sort | 3515 243 221 |
| 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>02376nam a2200613 c 4500</leader><controlfield tag="001">BV011849152</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20010920 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">980317s1998 gw |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">953180531</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764359366</subfield><subfield code="9">3-7643-5936-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817659366</subfield><subfield code="9">0-8176-5936-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)38910271</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011849152</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="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-526</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA312.B53 1998</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.43 21</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.43</subfield><subfield code="2">21</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">27</subfield><subfield code="2">sdnb</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">Bichteler, Klaus</subfield><subfield code="d">1938-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)106060279</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integration - a functional approach</subfield><subfield code="c">Klaus Bichteler</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 193 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="0" ind2=" "><subfield code="a">Birkhäuser advanced texts</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integrals</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="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">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lebesgue-Integral</subfield><subfield code="0">(DE-588)4034949-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Riemannsches Integral</subfield><subfield code="0">(DE-588)4049996-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" 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="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" 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="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Riemannsches Integral</subfield><subfield code="0">(DE-588)4049996-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="4" ind2="0"><subfield code="a">Lebesgue-Integral</subfield><subfield code="0">(DE-588)4034949-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="4" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</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=008003466&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:BVB01-008003466</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV011849152 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:17:24Z |
| institution | BVB |
| isbn | 3764359366 0817659366 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008003466 |
| oclc_num | 38910271 |
| open_access_boolean | |
| owner | DE-384 DE-20 DE-739 DE-29T DE-824 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-521 DE-526 DE-634 DE-188 |
| owner_facet | DE-384 DE-20 DE-739 DE-29T DE-824 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-521 DE-526 DE-634 DE-188 |
| physical | VIII, 193 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Birkhäuser advanced texts |
| spelling | Bichteler, Klaus 1938- Verfasser (DE-588)106060279 aut Integration - a functional approach Klaus Bichteler Basel [u.a.] Birkhäuser 1998 VIII, 193 S. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Integrals Measure theory Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 gnd rswk-swf Riemannsches Integral (DE-588)4049996-0 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 s DE-604 Integrationstheorie (DE-588)4138369-2 s Maßtheorie (DE-588)4074626-4 s Riemannsches Integral (DE-588)4049996-0 s 1\p DE-604 Lebesgue-Integral (DE-588)4034949-4 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008003466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bichteler, Klaus 1938- Integration - a functional approach Integrals Measure theory Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Riemannsches Integral (DE-588)4049996-0 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4072852-3 (DE-588)4074626-4 (DE-588)4034949-4 (DE-588)4049996-0 |
| title | Integration - a functional approach |
| title_auth | Integration - a functional approach |
| title_exact_search | Integration - a functional approach |
| title_full | Integration - a functional approach Klaus Bichteler |
| title_fullStr | Integration - a functional approach Klaus Bichteler |
| title_full_unstemmed | Integration - a functional approach Klaus Bichteler |
| title_short | Integration - a functional approach |
| title_sort | integration a functional approach |
| topic | Integrals Measure theory Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Riemannsches Integral (DE-588)4049996-0 gnd |
| topic_facet | Integrals Measure theory Integrationstheorie Integration Mathematik Maßtheorie Lebesgue-Integral Riemannsches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008003466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bichtelerklaus integrationafunctionalapproach |