Strange functions in real analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2005
|
| Edition: | 2. ed. |
| Series: | Pure and applied mathematics
277 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 415 S. |
| ISBN: | 1584885823 |
Staff View
MARC
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| 245 | 1 | 0 | |a Strange functions in real analysis |c A. B. Kharazishvili |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2005 | |
| 300 | |a XII, 415 S. | ||
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| 490 | 1 | |a Pure and applied mathematics |v 277 | |
| 500 | |a Includes bibliographical references and index | ||
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Record in the Search Index
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| adam_text | Table of Contents
Preface
Introductions basic concepts
1.
2.
3.
countably continuous
4.
5.
functions
6.
7.
functions
8.
without the Baire property
9.
10.
11.
12.
XI
XÜ
13.
14.
15.
functions
16.
operators
17.
right-hand sides
18.
of view of category and measure
Bibliography
Subject Index
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue
integrable
nonintegrable Lebesgue measurable functions. While dubbed strange
or pathological, these functions are ubiquitous throughout mathematics
and play an important role in analysis, not only as counterexamples of
seemingly true and natural statements, but also to stimulate and inspire
the further development of real analysis.
Strange Functions in Real Analysis explores a number of important
examples and constructions of pathological functions! After introducing
the basic concepts, the author begins with Cantor and Peano-type
functions, then moves to functions whose constructions require essentially
noneffective methods. These include functions without the Baire property,
Junctions associated with a Hamel basis of the real line, and Sierpinski-.
Zygmund functions that are discontinuous on each subset of the real
Mine having the cardinality continuum. Finally, he considers examples of
functions whose existence cannot be established without thejielp of
additional set-theoretical axioms and demonstrates that their existence
1
Hypothesis.!
I New in the Second Edition;
Five new chapters that provide mote information on the structure ot
pathological functions WKWa^mmmmmtmm^Fl^mm
Refined and expanded discussions thioughout the text
Nearly
discussions within the text and point out deep relationships between
them ^IBI^^^^t^^^B^^^Sil^atsiaiaia^ia^^^jjigi^ii^^^ipiJi^^i^^g^mmiff^jffjT^ij^^
A significantly expanded list of references that incorporates receipt
works
|
| adam_txt |
Table of Contents
Preface
Introductions basic concepts
1.
2.
3.
countably continuous
4.
5.
functions
6.
7.
functions
8.
without the Baire property
9.
10.
11.
12.
XI
XÜ
13.
14.
15.
functions
16.
operators
17.
right-hand sides
18.
of view of category and measure
Bibliography
Subject Index
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue
integrable
nonintegrable Lebesgue measurable functions. While dubbed strange
or "pathological," these functions are ubiquitous throughout mathematics
and play an important role in analysis, not only as counterexamples of
seemingly true and natural statements, but also to stimulate and inspire'
the further development of real analysis.
Strange Functions in Real Analysis explores a number of important
examples and constructions of pathological functions! After introducing
the basic concepts, the author begins with Cantor and Peano-type
functions,'then moves to functions whose constructions require essentially
noneffective methods. These include functions without the Baire property,
Junctions associated with a Hamel basis of the real line, and Sierpinski-.
Zygmund functions that are discontinuous on each subset of the real
Mine having the cardinality continuum. Finally, he considers examples of
functions whose existence cannot be established without thejielp of
additional set-theoretical axioms and demonstrates that their existence
1
Hypothesis.!
I New in the Second Edition;
Five new chapters that provide mote information on the structure ot
pathological functions WKWa^mmmmmtmm^Fl^mm
Refined and expanded discussions thioughout the text
Nearly
discussions within the text and point out deep relationships between
them ^IBI^^^^t^^^B^^^Sil^atsiaiaia^ia^^^jjigi^ii^^^ipiJi^^i^^g^mmiff^jffjT^ij^^
A significantly expanded list of references that incorporates receipt
works |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:04:41Z |
| indexdate | 2024-07-09T20:36:07Z |
| institution | BVB |
| isbn | 1584885823 |
| language | English |
| lccn | 2005053715 |
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| physical | XII, 415 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Charazišvili, Aleksandr Bežanovič 1949- Verfasser (DE-588)1058151622 aut Strange functions in real analysis A. B. Kharazishvili 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2005 XII, 415 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 277 Includes bibliographical references and index Functional analysis Functions of real variables Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 s DE-604 Pure and applied mathematics 277 (DE-604)BV000001885 277 Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014663541&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014663541&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Charazišvili, Aleksandr Bežanovič 1949- Strange functions in real analysis Pure and applied mathematics Functional analysis Functions of real variables Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4627581-2 |
| title | Strange functions in real analysis |
| title_auth | Strange functions in real analysis |
| title_exact_search | Strange functions in real analysis |
| title_exact_search_txtP | Strange functions in real analysis |
| title_full | Strange functions in real analysis A. B. Kharazishvili |
| title_fullStr | Strange functions in real analysis A. B. Kharazishvili |
| title_full_unstemmed | Strange functions in real analysis A. B. Kharazishvili |
| title_short | Strange functions in real analysis |
| title_sort | strange functions in real analysis |
| topic | Functional analysis Functions of real variables Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Functional analysis Functions of real variables Reelle Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014663541&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=014663541&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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