Verfügbarkeit: Algebraic theory of measure and integration

Algebraic theory of measure and integration:

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Carathéodory, Constantin 1873-1950 (VerfasserIn)
Weitere Verfasser:	Finsler, Paul 1894-1970 (HerausgeberIn)
Format:	Buch
Sprache:	English German
Veröffentlicht:	Providence, RI American Mathematical Society 2010
Ausgabe:	2. English ed.
Schlagworte:	Integrationstheorie Maßtheorie Algebra Integral
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Verl. auf der Haupttitels. außerdem: Chelsa Publ.
Beschreibung:	378 S. 24 cm
ISBN:	9780821852736 0821852736

Internformat

MARC


LEADER	00000nam a2200000 c 4500
001	BV041767538
003	DE-604
005	20140509
007	t
008	140331s2010 xxu \|\|\|\| 00\|\|\| eng d
015			\|a 14,A10 \|2 dnb
016	7		\|a 1026888468 \|2 DE-101
020			\|a 9780821852736 \|c Pp. \|9 978-0-8218-5273-6
020			\|a 0821852736 \|9 0-8218-5273-6
035			\|a (OCoLC)880303684
035			\|a (DE-599)DNB1026888468
040			\|a DE-604 \|b ger \|e rakddb
041	1		\|a eng \|h ger
044			\|a xxu \|c XD-US
049			\|a DE-739
082	0		\|a 515.42 \|2 22/ger
084			\|a 510 \|2 sdnb
100	1		\|a Carathéodory, Constantin \|d 1873-1950 \|e Verfasser \|0 (DE-588)118667076 \|4 aut
240	1	0	\|a Mass und Integral und ihre Algebraisierung
245	1	0	\|a Algebraic theory of measure and integration \|c C. Carathéodory. [Ed. P. Finsler ... Transl. by F. E. J. Linton. American Mathematical Society]
250			\|a 2. English ed.
264		1	\|a Providence, RI \|b American Mathematical Society \|c 2010
300			\|a 378 S. \|c 24 cm
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
500			\|a Verl. auf der Haupttitels. außerdem: Chelsa Publ.
650	0	7	\|a Integrationstheorie \|0 (DE-588)4138369-2 \|2 gnd \|9 rswk-swf
650	0	7	\|a Maßtheorie \|0 (DE-588)4074626-4 \|2 gnd \|9 rswk-swf
650	0	7	\|a Algebra \|0 (DE-588)4001156-2 \|2 gnd \|9 rswk-swf
650	0	7	\|a Integral \|0 (DE-588)4131477-3 \|2 gnd \|9 rswk-swf
689	0	0	\|a Maßtheorie \|0 (DE-588)4074626-4 \|D s
689	0	1	\|a Integrationstheorie \|0 (DE-588)4138369-2 \|D s
689	0		\|5 DE-604
689	1	0	\|a Maßtheorie \|0 (DE-588)4074626-4 \|D s
689	1	1	\|a Algebra \|0 (DE-588)4001156-2 \|D s
689	1		\|8 1\p \|5 DE-604
689	2	0	\|a Integral \|0 (DE-588)4131477-3 \|D s
689	2		\|8 2\p \|5 DE-604
700	1		\|a Finsler, Paul \|d 1894-1970 \|0 (DE-588)118533150 \|4 edt
856	4	2	\|m DNB Datenaustausch \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027213585&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-027213585
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

Datensatz im Suchindex

_version_	1804152075161960448
adam_text	CONTENTS PREFACE 3 EDITORS PREFACE 4 TRANSLATOR S PREFACE 6 I. SOMAS H §§ 1-2. THE AXIOMATIC METHOD 11 §§ 3-7. ELEMENTARY THEORY OF SOMAS 13 §§ 8-13. SOMAS AS ELEMENTS OF A BOOLEAN ALGEBRA 20 §§ 14-16. THE MAIN PROPERTIES OF THE UNION 27 §§ 17-22. THE DECOMPOSABILITY OF SOMAS 31 §§ 23-24. THE INTERSECTION OF AN INFINITE NUMBER OF SOMAS. . 37 §§ 25-32. LIMITS AND BOUNDS 41 II. SETS OF SOMAS 52 §§33-40. SETS OF SOMAS CLOSED UNDER A BINARY OPERATION. . 52 §§41-46. COMPLETE RINGS 58 §§ 47-53. ORDINAL NUMBERS OF THE SECOND CLASS 62 §§ 54-55. HEREDITARY SETS OF SOMAS 68 §§ 56-64. HOMOMORPHISMS OF RINGS OF SOMAS 70 III. PLACE FUNCTIONS 82 §§65-68. FINITELY-VALUED PLACE FUNCTIONS 82 §§69-75. NESTS OF SOMAS 86 §§ 76-79. ALTERING THE DOMAIN OF DEFINITION 95 §§ 80-88. PRINCIPAL PROPERTIES OF THE SOMA FUNCTIONS A(X) AND /8(X) 100 IV. CALCULATION WITH PLACE FUNCTIONS . 112 §§ 89-94. LIMIT PROCESSES 112 §§ 95-106. ELEMENTARY OPERATIONS ON PLACE FUNCTIONS 119 §§ 107-110. UNIFORM AND ABSOLUTE CONVERGENCE 133 §§111-117. COMPOSITION OF PLACE FUNCTIONS 136 §§ 118-125. HOMOMORPHISMS OF PLACE FUNCTIONS 147 HTTP://D-NB.INFO/1026888468 8 CONTENTS V. MEASURE FUNCTIONS 157 §§ 126-128. ADDITIVE AND UNION-BOUNDED SOMA FUNCTIONS... 157 §§ 129-130. MEASURABILITY 161 §§ 131-135. MEASURE FUNCTIONS 163 §§ 136-140. THE MEASURE FUNCTION ON ITS RING OF MEASURABILITY 169 §§ 141-143. SEQUENCES OF MEASURE FUNCTIONS AND THEIR LIMITS 173 §§ 144-147. TRANSFORMATION OF MEASURE FUNCTIONS BY HOMO- MORPHISMS 175 §§ 148-153. THE BOREL-LEBESGUE CONTENT 179 VI. THE INTEGRAL 188 § 154. FIELDS OF PLACE FUNCTIONS; MEASURABLE PLACE FUNC TIONS 188 §§ 155-162. THE NOTION OF THE INTEGRAL 189 §§ 163-166. LINEARITY OF THE INTEGRAL AND THE INTEGRATION OF PLACE FUNCTIONS OF ARBITRARY SIGN 199 §§ 167-172. COMPARABLE MEASURE FUNCTIONS AND THE LEBESGUE DECOMPOSITION 203 §§ 173-175. ABSTRACT DIFFERENTIALS 210 §§ 176-177. THE ABSOLUTE CONTINUITY OF TWO COMPARABLE MEASURE FUNCTIONS 212 §§ 178-180. TRANSFORMATION OF THE INTEGRAL BY MEANS OF HOMOMORPHISMS 214 VII. APPLICATION OF THE THEORY OF INTEGRATION TO LIMIT PROCESSES 219 §§ 181-183. THE THEOREM OF EGOROFF 219 §§ 184-189. CONTINUITY OF THE INTEGRAL AS A FUNCTIONAL 224 §§ 190-197. CONVERGENCE IN THE MEAN 233 §§ 198-205. ERGODIC THEORY 240 VIII. THE COMPUTATION OF MEASURE FUNCTIONS 253 §§206-210. MAXIMAL MEASURE FUNCTIONS 253 §§ 211-215. THE BASES OF AN ARBITRARY MEASURE FUNCTION.... 257 §§216-221. RELATIVE MEASURABILITY 261 IX. REGULAR MEASURE FUNCTIONS 268 §§ 222-224. THE DEFINITION AND PRINCIPAL PROPERTIES OF REGU LAR MEASURE FUNCTIONS 268 §§ 225-229. INNER MEASURE 272 §§230-235. COMPARISON OF INNER AND OUTER MEASURES 278 §§ 236-240. THE ARITHMETIC MEAN OF THE INNER AND OUTER MEASURES . 283 CONTENTS 9 X. ISOTYPIC REGULAR MEASURE FUNCTIONS 288 §§241-244. THE PRINCIPAL PROPERTIES OF ISOTYPIC MEASURE FUNCTIONS 288 §§ 245-248. THE JORDAN DECOMPOSITION OF COMPLETELY ADDITIVE SOMA FUNCTIONS 293 §§ 249-255. THE DIFFERENCE OF TWO ISOTYPIC REGULAR MEASURE FUNCTIONS 299 §§256-257. COMPARABLE OUTER MEASURES 306 XI. CONTENT FUNCTIONS 310 §§258-259. THE DEFINITION OF CONTENT FUNCTIONS 310 §§ 260-267. REDUCED CONTENT FUNCTIONS AND THEIR HOMO- MORPHISMS 313 §§268-271. THE JESSEN INFINITE-DIMENSIONAL TORUS 320 §§ 272-278. THE VITALI COVERING THEOREM 322 §§279-282. THE LEBESGUE INTEGRAL 331 §§283-284. COMPARABLE CONTENT FUNCTIONS 337 §§ 285-289. LINEAR MEASURE 339 APPENDIX: SOMAS AS ELEMENTS OF PARTIALLY ORDERED SETS 345 §§ 290-297. A NEW AXIOM SYSTEM FOR SOMAS 345 §§ 298-302. THE PARTITIONING OF A SET INTO CLASSES 353 §§ 303-304. PARTIALLY ORDERED SETS 356 §§ 305-308. APPLICATIONS TO THE THEORY OF SOMAS 359 §§ 309-312. SYSTEMS OF SOMAS THAT ARE NOT ISOMORPHIC TO SYS TEMS OF SUBSETS OF A SET 362 BIBLIOGRAPHY : EARLIER PUBLICATIONS BY CONSTANTIN CARATHEODORY ON THE ALGEBRAIZATION OF MEASURE AND INTEGRAL 369 LIST OF SYMBOLS 371 INDEX 373
any_adam_object	1
author	Carathéodory, Constantin 1873-1950
author2	Finsler, Paul 1894-1970
author2_role	edt
author2_variant	p f pf
author_GND	(DE-588)118667076 (DE-588)118533150
author_facet	Carathéodory, Constantin 1873-1950 Finsler, Paul 1894-1970
author_role	aut
author_sort	Carathéodory, Constantin 1873-1950
author_variant	c c cc
building	Verbundindex
bvnumber	BV041767538
ctrlnum	(OCoLC)880303684 (DE-599)DNB1026888468
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
edition	2. English ed.
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02269nam a2200553 c 4500</leader><controlfield tag="001">BV041767538</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20140509 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">140331s2010 xxu \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">14,A10</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1026888468</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821852736</subfield><subfield code="c">Pp.</subfield><subfield code="9">978-0-8218-5273-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821852736</subfield><subfield code="9">0-8218-5273-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)880303684</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1026888468</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="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.42</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Carathéodory, Constantin</subfield><subfield code="d">1873-1950</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)118667076</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Mass und Integral und ihre Algebraisierung</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic theory of measure and integration</subfield><subfield code="c">C. Carathéodory. [Ed. P. Finsler ... Transl. by F. E. J. Linton. American Mathematical Society]</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. English ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">378 S.</subfield><subfield code="c">24 cm</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="500" ind1=" " ind2=" "><subfield code="a">Verl. auf der Haupttitels. außerdem: Chelsa Publ.</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">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">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" 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="0" ind2="1"><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">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Integral</subfield><subfield code="0">(DE-588)4131477-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Finsler, Paul</subfield><subfield code="d">1894-1970</subfield><subfield code="0">(DE-588)118533150</subfield><subfield code="4">edt</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB 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=027213585&sequence=000001&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:BVB01-027213585</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.BV041767538
illustrated	Not Illustrated
indexdate	2024-07-10T01:04:56Z
institution	BVB
isbn	9780821852736 0821852736
language	English German
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-027213585
oclc_num	880303684
open_access_boolean
owner	DE-739
owner_facet	DE-739
physical	378 S. 24 cm
publishDate	2010
publishDateSearch	2010
publishDateSort	2010
publisher	American Mathematical Society
record_format	marc
spelling	Carathéodory, Constantin 1873-1950 Verfasser (DE-588)118667076 aut Mass und Integral und ihre Algebraisierung Algebraic theory of measure and integration C. Carathéodory. [Ed. P. Finsler ... Transl. by F. E. J. Linton. American Mathematical Society] 2. English ed. Providence, RI American Mathematical Society 2010 378 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Verl. auf der Haupttitels. außerdem: Chelsa Publ. Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Integral (DE-588)4131477-3 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s DE-604 Algebra (DE-588)4001156-2 s 1\p DE-604 Integral (DE-588)4131477-3 s 2\p DE-604 Finsler, Paul 1894-1970 (DE-588)118533150 edt DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027213585&sequence=000001&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	Carathéodory, Constantin 1873-1950 Algebraic theory of measure and integration Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd Algebra (DE-588)4001156-2 gnd Integral (DE-588)4131477-3 gnd
subject_GND	(DE-588)4138369-2 (DE-588)4074626-4 (DE-588)4001156-2 (DE-588)4131477-3
title	Algebraic theory of measure and integration
title_alt	Mass und Integral und ihre Algebraisierung
title_auth	Algebraic theory of measure and integration
title_exact_search	Algebraic theory of measure and integration
title_full	Algebraic theory of measure and integration C. Carathéodory. [Ed. P. Finsler ... Transl. by F. E. J. Linton. American Mathematical Society]
title_fullStr	Algebraic theory of measure and integration C. Carathéodory. [Ed. P. Finsler ... Transl. by F. E. J. Linton. American Mathematical Society]
title_full_unstemmed	Algebraic theory of measure and integration C. Carathéodory. [Ed. P. Finsler ... Transl. by F. E. J. Linton. American Mathematical Society]
title_short	Algebraic theory of measure and integration
title_sort	algebraic theory of measure and integration
topic	Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd Algebra (DE-588)4001156-2 gnd Integral (DE-588)4131477-3 gnd
topic_facet	Integrationstheorie Maßtheorie Algebra Integral
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027213585&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT caratheodoryconstantin massundintegralundihrealgebraisierung AT finslerpaul massundintegralundihrealgebraisierung AT caratheodoryconstantin algebraictheoryofmeasureandintegration AT finslerpaul algebraictheoryofmeasureandintegration

Verfügbarkeit

Es ist kein Print-Exemplar vorhanden.

Fernleihe Bestellen Achtung: Nicht im THWS-Bestand! Inhaltsverzeichnis

MARC

Datensatz im Suchindex

Es ist kein Print-Exemplar vorhanden.

Ähnliche Einträge