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Real analysis:

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Bibliographic Details
Main Author:	Loeb, Peter A. (Author)
Format:	Electronic eBook
Language:	English
Published:	[Basel] Birkhäuser [2016]
Subjects:	Mathematics Functional analysis Measure theory Functions of real variables Real Functions Functional Analysis Measure and Integration Mathematik
Online Access:	BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource (XII, 274 Seiten)
ISBN:	9783319307442
DOI:	10.1007/978-3-319-30744-2

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MARC


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Record in the Search Index

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adam_text	REAL ANALYSIS / LOEB, PETER A. : 2016 TABLE OF CONTENTS / INHALTSVERZEICHNIS PREFACE SET THEORY AND NUMBERS MEASURE ON THE REAL LINE MEASURABLE FUNCTIONS INTEGRATION DIFFERENTIATION AND INTEGRATION GENERAL MEASURE SPACES INTRODUCTION TO METRIC AND NORMED SPACES HILBERT SPACES TOPOLOGICAL SPACES MEASURE CONSTRUCTION BANACH SPACES APPENDICES REFERENCES. DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. REAL ANALYSIS / LOEB, PETER A. : 2016 ABSTRACT / INHALTSTEXT THIS TEXTBOOK IS DESIGNED FOR A YEAR-LONG COURSE IN REAL ANALYSIS TAKEN BY BEGINNING GRADUATE AND ADVANCED UNDERGRADUATE STUDENTS IN MATHEMATICS AND OTHER AREAS SUCH AS STATISTICS, ENGINEERING, AND ECONOMICS. WRITTEN BY ONE OF THE LEADING SCHOLARS IN THE FIELD, IT ELEGANTLY EXPLORES THE CORE CONCEPTS IN REAL ANALYSIS AND INTRODUCES NEW, ACCESSIBLE METHODS FOR BOTH STUDENTS AND INSTRUCTORS. THE FIRST HALF OF THE BOOK DEVELOPS BOTH LEBESGUE MEASURE AND, WITH ESSENTIALLY NO ADDITIONAL WORK FOR THE STUDENT, GENERAL BOREL MEASURES FOR THE REAL LINE. NOTATION INDICATES WHEN A RESULT HOLDS ONLY FOR LEBESGUE MEASURE. DIFFERENTIATION AND ABSOLUTE CONTINUITY ARE PRESENTED USING A LOCAL MAXIMAL FUNCTION, RESULTING IN AN EXPOSITION THAT IS BOTH SIMPLER AND MORE GENERAL THAN THE TRADITIONAL APPROACH. THE SECOND HALF DEALS WITH GENERAL MEASURES AND FUNCTIONAL ANALYSIS, INCLUDING HILBERT SPACES, FOURIER SERIES, AND THE RIESZ REPRESENTATION THEOREM FOR POSITIVE LINEAR FUNCTIONALS ON CONTINUOUS FUNCTIONS WITH COMPACT SUPPORT. TO CORRECTLY DISCUSS WEAK LIMITS OF MEASURES, ONE NEEDS THE NOTION OF A TOPOLOGICAL SPACE RATHER THAN JUST A METRIC SPACE, SO GENERAL TOPOLOGY IS INTRODUCED IN TERMS OF A BASE OF NEIGHBORHOODS AT A POINT. THE DEVELOPMENT OF RESULTS THEN PROCEEDS IN PARALLEL WITH RESULTS FOR METRIC SPACES, WHERE THE BASE IS GENERATED BY BALLS CENTERED AT A POINT. THE TEXT CONCLUDES WITH APPENDICES ON COVERING THEOREMS FOR HIGHER DIMENSIONS AND A SHORT INTRODUCTION TO NONSTANDARD ANALYSIS INCLUDING IMPORTANT APPLICATIONS TO PROBABILITY THEORY AND MATHEMATICAL ECONOMICS. DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
any_adam_object	1
author	Loeb, Peter A.
author_facet	Loeb, Peter A.
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author_sort	Loeb, Peter A.
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dewey-full	515.8
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515.8
dewey-search	515.8
dewey-sort	3515.8
dewey-tens	510 - Mathematics
discipline	Mathematik
doi_str_mv	10.1007/978-3-319-30744-2
format	Electronic eBook
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illustrated	Not Illustrated
indexdate	2024-07-10T07:29:22Z
institution	BVB
isbn	9783319307442
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-028994408
oclc_num	951066232
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owner	DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-739 DE-634 DE-898 DE-BY-UBR DE-861 DE-703 DE-824 DE-83
owner_facet	DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-739 DE-634 DE-898 DE-BY-UBR DE-861 DE-703 DE-824 DE-83
physical	1 Online-Ressource (XII, 274 Seiten)
psigel	ZDB-2-SMA ZDB-2-SMA_2016
publishDate	2016
publishDateSearch	2016
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publisher	Birkhäuser
record_format	marc
spelling	Loeb, Peter A. Verfasser aut Real analysis Peter A. Loeb [Basel] Birkhäuser [2016] © 2016 1 Online-Ressource (XII, 274 Seiten) txt rdacontent c rdamedia cr rdacarrier Mathematics Functional analysis Measure theory Functions of real variables Real Functions Functional Analysis Measure and Integration Mathematik Erscheint auch als Druckausgabe 978-3-319-30742-8 https://doi.org/10.1007/978-3-319-30744-2 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994408&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994408&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract
spellingShingle	Loeb, Peter A. Real analysis Mathematics Functional analysis Measure theory Functions of real variables Real Functions Functional Analysis Measure and Integration Mathematik
title	Real analysis
title_auth	Real analysis
title_exact_search	Real analysis
title_full	Real analysis Peter A. Loeb
title_fullStr	Real analysis Peter A. Loeb
title_full_unstemmed	Real analysis Peter A. Loeb
title_short	Real analysis
title_sort	real analysis
topic	Mathematics Functional analysis Measure theory Functions of real variables Real Functions Functional Analysis Measure and Integration Mathematik
topic_facet	Mathematics Functional analysis Measure theory Functions of real variables Real Functions Functional Analysis Measure and Integration Mathematik
url	https://doi.org/10.1007/978-3-319-30744-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994408&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994408&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT loebpetera realanalysis

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