Holdings: Modern theories of integration

Modern theories of integration:

Saved in:

Bibliographic Details
Main Author:	Kestelman, Hyman (Author)
Format:	Book
Language:	English
Published:	New York Dover Publ. 1960
Edition:	2., rev. ed.
Series:	Dover books on advanced mathematics
Subjects:	Intégrales généralisées Integrals, Generalized Integrationstheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 308 S.

Staff View

MARC


LEADER	00000nam a2200000 c 4500
001	BV006247731
003	DE-604
005	19980202
007	t
008	930210s1960 \|\|\|\| 00\|\|\| eng d
035			\|a (OCoLC)253461
035			\|a (DE-599)BVBBV006247731
040			\|a DE-604 \|b ger \|e rakddb
041	0		\|a eng
049			\|a DE-739 \|a DE-355 \|a DE-20 \|a DE-83
050		0	\|a QA312
082	0		\|a 517.3
084			\|a SK 430 \|0 (DE-625)143239: \|2 rvk
100	1		\|a Kestelman, Hyman \|e Verfasser \|4 aut
245	1	0	\|a Modern theories of integration \|c by H. Kestelman
250			\|a 2., rev. ed.
264		1	\|a New York \|b Dover Publ. \|c 1960
300			\|a X, 308 S.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	0		\|a Dover books on advanced mathematics
650		4	\|a Intégrales généralisées
650		4	\|a Integrals, Generalized
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
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=003945203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-003945203

Record in the Search Index

_version_	1804120461734313984
adam_text	CONTENTS I. SETS OF POINTS ...... 1 § 1. Real numbers ...... 1 § 2. Sets of points ...... 2 § 3. Equivalence of aggregates . . . . 8 §4. Metrical properties of Rn. . . . .13 § 5. The Selection Axiom . . . . .28 § 6. General Principle of Convergence in Rn . . .29 II. RIEMANN INTEGRATION . . . . .30 §1. Functions defined in a set of points . . .30 § 2. Definition of Riemann integral . . . .32 § 3. Conditions for a function to be integrable iJ . . 36 § 4. Properties of the Riemann integral . . .42 § 5. Riemann integration of derivatives . . .46 § 6. Riemann integration of limit functions . . .50 § 7. Cauchy Riemann integral . . .54 § 8. Geometric interpretation of Riemann integration. . 55 III. LEBESGUE MEASURE . . . . .67 § 1. Exterior Lebesgue measure . . . .67 § 2. Measurable sets . . . . . .70 § 3. Interior Lebesgue measure . . . .80 § 4. Linear transformations . . . . .87 § 5. Non measurable sets . . . . .89 IV. SETS OF ORDINATES AND MEASURABLE FUNCTIONS 92 § 1. Sets of ordinates . . . . . .92 § 2. Cylinder sets . . . . . .94 § 3. Measurable functions . . . . .96 § 4. Lusin s theorem ...... 109 V. LEBESGUE INTEGRAL OF A NON NEGATIVE FUNCTION 113 VI. LEBESGUE INTEGRALS OF FUNCTIONS WHICH ARE SOMETIMES NEGATIVE . . . .128 § 1. Real functions . . . . . .128 § 2. Complex functions ..... 156 VII. FUNCTIONS OF A SINGLE VARIABLE . . .161 § 1. Miscellaneous theorems: integration by parts, second mean value theorem, differentiation under the integral sign . 161 § 2. Derivative of a Lebesgue integral . . .172 § 3. Summability of derivatives .... 174 § 4. Bounded variation and absolute continuity . .184 § 5. Integration by substitution .... 192 § 6. Appendix to § 3 . . . . . .199 VIII. EVALUATION OF DOUBLE INTEGRALS . . .202 x CONTENTS IX. EXTENSIONS OF THE LEBESGUE INTEGRAL . .213 § 1. Holder Lebesgue integral . . . .213 § 2. General Denjoy integral ..... 217 X. FOURIER SERIES . . . . . .228 § 1. Introduction ...... 228 § 2. Convergence tests ..... 232 § 3. Summability (C, 1) of Fourier series . . . 240 §4. Integration of Fourier series . . . .241 § 5. Trigonometric and Fourier series. . . . 243 XI. RIEMANN STIELTJES INTEGRATION . . .247 § 1. Introduction . . . . . .247 § 2. The Riemann Stieltjes integral .... 248 § 3. Properties of the Riemann Stieltjes integral . . 251 § 4. Applications of Stieltjes integration . . . 262 § 5 . Riesz s theorem ...... 265 EXERCISES . . . . . . .270 BIBLIOGRAPHY . . . . . .303 INDEX OF DEFINITIONS AND SYMBOLS . . .304 GENERAL INDEX . . . . . .306 INDEX TO THE EXERCISES . . . .309 SET THEORY NOTATION The principal differences between the notation in the text and that in current use are noted below. The intersection AB is now usually denoted by A n B and UAr by j \| Ar. Similarly A+B and A + B t r may be denoted by A U B and £4r by JAr. The symbol A is now r r generally used to denote the closure of A, i.e. A U A (denoted in the text by Ac [def.2O]); the complement of A (denoted in the text by A) is then denoted by C(A).
any_adam_object	1
author	Kestelman, Hyman
author_facet	Kestelman, Hyman
author_role	aut
author_sort	Kestelman, Hyman
author_variant	h k hk
building	Verbundindex
bvnumber	BV006247731
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)253461 (DE-599)BVBBV006247731
dewey-full	517.3
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	517 - [Unassigned]
dewey-raw	517.3
dewey-search	517.3
dewey-sort	3517.3
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	2., rev. ed.
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01311nam a2200373 c 4500</leader><controlfield tag="001">BV006247731</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19980202 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930210s1960 \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)253461</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV006247731</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-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA312</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">517.3</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="100" ind1="1" ind2=" "><subfield code="a">Kestelman, Hyman</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Modern theories of integration</subfield><subfield code="c">by H. Kestelman</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2., rev. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Dover Publ.</subfield><subfield code="c">1960</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 308 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">Dover books on advanced mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Intégrales généralisées</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integrals, Generalized</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="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=003945203&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:BVB01-003945203</subfield></datafield></record></collection>
id	DE-604.BV006247731
illustrated	Not Illustrated
indexdate	2024-07-09T16:42:28Z
institution	BVB
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-003945203
oclc_num	253461
open_access_boolean
owner	DE-739 DE-355 DE-BY-UBR DE-20 DE-83
owner_facet	DE-739 DE-355 DE-BY-UBR DE-20 DE-83
physical	X, 308 S.
publishDate	1960
publishDateSearch	1960
publishDateSort	1960
publisher	Dover Publ.
record_format	marc
series2	Dover books on advanced mathematics
spelling	Kestelman, Hyman Verfasser aut Modern theories of integration by H. Kestelman 2., rev. ed. New York Dover Publ. 1960 X, 308 S. txt rdacontent n rdamedia nc rdacarrier Dover books on advanced mathematics Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003945203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Kestelman, Hyman Modern theories of integration Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd
subject_GND	(DE-588)4138369-2
title	Modern theories of integration
title_auth	Modern theories of integration
title_exact_search	Modern theories of integration
title_full	Modern theories of integration by H. Kestelman
title_fullStr	Modern theories of integration by H. Kestelman
title_full_unstemmed	Modern theories of integration by H. Kestelman
title_short	Modern theories of integration
title_sort	modern theories of integration
topic	Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd
topic_facet	Intégrales généralisées Integrals, Generalized Integrationstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003945203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT kestelmanhyman moderntheoriesofintegration

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Indexes

MARC

Record in the Search Index

There is no print copy available.

Similar Items