Set theoretical aspects of real analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2015
|
| Schriftenreihe: | Monographs and research notes in mathematics
A Chapman & Hall book |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXII, 433 S. |
| ISBN: | 9781482242010 |
Internformat
MARC
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| 245 | 1 | 0 | |a Set theoretical aspects of real analysis |c Alexander B. Kharazishvili |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2015 | |
| 300 | |a XXII, 433 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Monographs and research notes in mathematics | |
| 490 | 0 | |a A Chapman & Hall book | |
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| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Set theory | |
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Datensatz im Suchindex
| _version_ | 1804152569174425600 |
|---|---|
| adam_text | Table
of
Contents
Preface
............................ix
1.
ZF
theory and some point sets on the real line
.... 1
2.
Countable versions of AC and real analysis
......21
3.
Uncountable versions of AC and
Lebesgue nonmeasurable sets
..............35
4.
The Continuum Hypothesis and
Łebesgue
nonmeasurable sets
..............53
5.
Measurability properties of sets and functions
.... 67
6.
Radon measures and nonmeasurable sets
.......87
7.
Real-valued step functions with strange
measurability properties
.................107
8.
A partition of the real line into
continuum many thick subsets
.............123
9.
Measurability properties of
Vitali
sets
.........137
10.
A relationship between the measurability
and continuity of real-valued functions
........151
11.
A relationship between
absolutely nonmeasurable functions and
Sierpiński—
Zygmund type functions
..........167
12.
Sums of absolutely nonmeasurable
injective functions
.....................181
VII
Viii TABLE OF
CONTENTS
13.
A large
group of absolutely
nonmeasurable additive functions...........
195
14.
Additive properties of certain classes of
pathological functions
.................. 209
15.
Absolutely nonmeasurable
hörnornor
phis ms
of commutative groups
..................225
16.
Measurable and nonmeasurable sets
with homogeneous sections
...............239
17.
A combinatorial problem on translation
invariant extensions of the Lebesgue measure
.... 253
18.
Countable almost invariant
partitions of G-spaces
...................269
19.
Nonmeasurable unions of measure zero
sections of plane sets
...................287
20.
Measurability properties of well-orderings
......299
Appendix
1:
The axioms
ofset
theory
........317
Appendix
2:
The Axiom of Choice and
Generalized Continuum Hypothesis
..........341
Appendix
3:
Martin s Axiom and
its consequences in real analysis
............355
Appendix
4:
c^i-dense subsets of the real line
.... 371
Appendix
5:
The beginnings
of descriptive set theory
.................381
Bibliography
........................411
Subject Index
.......................429
Mathematics
MONOGRAPHS AND RESEARCH NOTES IN MATHEMATICS
Set Theoretical Aspects of Real Analysis is built around a number of ques¬
tions in real analysis and classical measure theory, which are of a set theoretic
flavor. Accessible to graduate students and researchers, the beginning of the
book presents introductory topics on real analysis and Lebesgue measure
theory. These topics highlight the boundary between fundamental concepts
of measurabitity and nonmeasurability for point sets and functions. The re¬
mainder of the book deals with more specialized material on set theoretical
real analysis.
The book focuses on certain logical and set theoretical aspects of real analy¬
sis. It is expected that the first eleven chapters can be used in a course on
Lebesgue measure theory that highlights the fundamental concepts of mea-
surability and nonmeasurability for point sets and functions. Provided in the
book are problems of varying difficulty that range from simple observations
to advanced results. Relatively difficult exercises are marked by asterisks and
hints are included with additional explanation. Five appendices are included
to supply additional background information that can be read alongside, be¬
fore, or after the chapters.
Features
•
Adopts a new ideology based on a classification of real-valued functions
(point sets) according to their measurability properties
•
Discusses the logical relationships between classical constructions of
Lebesgue nonmeasureable sets
•
Covers the structure of absolutely nonmeasurable real-valued functions
•
Presents a characteristic of ail commutative groups that admit
absolutely nonmeasurable homomorphisms into the real line
•
Explores interesting and unexpected connections between
combinatorics and translation-invariant extensions of the Lebesgue
measure
Dealing with classical concepts, the book highlights material not often found
in analysis courses. It lays out. in a logical, systematic manner, the founda¬
tions of set theory providing a readable treatment accessible to graduate stu¬
dents and researchers.
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042103792 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:12:48Z |
| institution | BVB |
| isbn | 9781482242010 |
| language | English |
| lccn | 014013375 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027544360 |
| oclc_num | 900486992 |
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| physical | XXII, 433 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Monographs and research notes in mathematics A Chapman & Hall book |
| spelling | Charazišvili, Aleksandr Bežanovič 1949- Verfasser (DE-588)1058151622 aut Set theoretical aspects of real analysis Alexander B. Kharazishvili Boca Raton [u.a.] CRC Press 2015 XXII, 433 S. txt rdacontent n rdamedia nc rdacarrier Monographs and research notes in mathematics A Chapman & Hall book Includes bibliographical references and index Mathematical analysis Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Mengenlehre (DE-588)4074715-3 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027544360&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027544360&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Charazišvili, Aleksandr Bežanovič 1949- Set theoretical aspects of real analysis Mathematical analysis Set theory Mengenlehre (DE-588)4074715-3 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4074715-3 (DE-588)4001865-9 |
| title | Set theoretical aspects of real analysis |
| title_auth | Set theoretical aspects of real analysis |
| title_exact_search | Set theoretical aspects of real analysis |
| title_full | Set theoretical aspects of real analysis Alexander B. Kharazishvili |
| title_fullStr | Set theoretical aspects of real analysis Alexander B. Kharazishvili |
| title_full_unstemmed | Set theoretical aspects of real analysis Alexander B. Kharazishvili |
| title_short | Set theoretical aspects of real analysis |
| title_sort | set theoretical aspects of real analysis |
| topic | Mathematical analysis Set theory Mengenlehre (DE-588)4074715-3 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Set theory Mengenlehre Analysis |
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