Scenes from the history of real functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1991
|
| Schriftenreihe: | Science networks
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | 265 S. |
| ISBN: | 3764325720 0817625720 |
Internformat
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| 100 | 1 | |a Medvedev, Fedor A. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Očerki istorii teorii funkcij dejstvitel'nogo peremennogo |
| 245 | 1 | 0 | |a Scenes from the history of real functions |c Fyodor A. Medvedev |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1991 | |
| 300 | |a 265 S. | ||
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| 490 | 1 | |a Science networks |v 7 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 7 | |a Fonctions d'une variable réelle - Histoire |2 ram | |
| 650 | 4 | |a Fonctions de variables réelles | |
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Datensatz im Suchindex
| _version_ | 1804118750311481344 |
|---|---|
| adam_text | Contents
Preface 9
Chapter 1 The place of the theory of functions of a real
variable among the mathematical disciplines
1.1 The subject matter of the theory of functions 11
1.2 Three periods in the development of
the theory of functions 13
1.3 The theory of functions and classical analysis 15
1.4 The theory of functions and functional analysis 18
1.5 The theory of functions and other
mathematical disciplines 22
Chapter 2 The history of the concept of a function
2.1 Some textbook definitions of the concept of a function 25
2.2 The concept of a function in ancient times and in the
Middle Ages 29
2.3 The seventeenth century origins of the concept
of a function 32
2.4 Some particular approaches to the concept of a function
in the seventeenth century 35
2.5 The Eulerian period in the development of the
concept of a function 40
2.6 Euler s contemporaries and heirs 44
2.7 The arbitrariness in a functional correspondence 50
2.8 The Lobachevskii Dirichlet definition 55
2.9 The extension and enrichment of the concept of a
function in the nineteenth century 63
2.10 The definition of a function according to Dedekind 67
2.11 Approaches to the concept of a function
from mathematical logic 70
2.12 Set functions 73
2.13 Some other functional correspondences 77
Chapter 3 Sequences of functions.
Various kinds of convergence
3.1 The analytic representation of a function 82
8 Contents
3.2 Simple uniform convergence . 85
3.3 Generalized uniform convergence 99
3.4 Arzela quasiuniform convergence 104
3.5 Convergence almost everywhere 110
3.6 Convergence in measure 120
3.7 Convergence in square mean. Harnack s
unsuccessful approach 128
3.8 Square mean convergence. The work of Fischer
and certain related investigations 137
3.9 Strong and weak convergence 145
3.10 The Baire classification 157
Chapter 4 The derivative and the integral
in their historical connection
4.1 Some general observations 168
4.2 Integral and differential methods up to the first half of the
seventeenth century 170
4.3 The analysis of Newton and Leibniz 177
4.4 The groundwork for separating the
concepts of derivative and integral 181
4.5 The separation of differentiation and integration 187
4.6 The Radon Nikodym theorem 198
4.7 The relation between differentiation and integration in the
works of Kolmogorov 202
4.8 The relation between differentiation and integration in the
works of Caratheodory 205
4.9 A few more general remarks 208
Chapter 5 Nondifferentiable continuous functions
5.1 Some introductory remarks 212
5.2 Ampere s theorem 214
5.3 Doubts and refutations 219
5.4 Classes of nondifferentiable functions 224
5.5 The relative smallness of the set
of differentiable functions 228
Bibliography 235
Index of names 260
|
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 18 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV004629790 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:15:15Z |
| institution | BVB |
| isbn | 3764325720 0817625720 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002842958 |
| oclc_num | 24796453 |
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| physical | 265 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Science networks |
| series2 | Science networks |
| spelling | Medvedev, Fedor A. Verfasser aut Očerki istorii teorii funkcij dejstvitel'nogo peremennogo Scenes from the history of real functions Fyodor A. Medvedev Basel [u.a.] Birkhäuser 1991 265 S. txt rdacontent n rdamedia nc rdacarrier Science networks 7 Aus d. Russ. übers. Fonctions d'une variable réelle - Histoire ram Fonctions de variables réelles Geschichte Functions of real variables History Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 s Geschichte (DE-588)4020517-4 s DE-604 Science networks 7 (DE-604)BV002495563 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002842958&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Medvedev, Fedor A. Scenes from the history of real functions Science networks Fonctions d'une variable réelle - Histoire ram Fonctions de variables réelles Geschichte Functions of real variables History Reelle Funktion (DE-588)4048918-8 gnd Geschichte (DE-588)4020517-4 gnd |
| subject_GND | (DE-588)4048918-8 (DE-588)4020517-4 |
| title | Scenes from the history of real functions |
| title_alt | Očerki istorii teorii funkcij dejstvitel'nogo peremennogo |
| title_auth | Scenes from the history of real functions |
| title_exact_search | Scenes from the history of real functions |
| title_full | Scenes from the history of real functions Fyodor A. Medvedev |
| title_fullStr | Scenes from the history of real functions Fyodor A. Medvedev |
| title_full_unstemmed | Scenes from the history of real functions Fyodor A. Medvedev |
| title_short | Scenes from the history of real functions |
| title_sort | scenes from the history of real functions |
| topic | Fonctions d'une variable réelle - Histoire ram Fonctions de variables réelles Geschichte Functions of real variables History Reelle Funktion (DE-588)4048918-8 gnd Geschichte (DE-588)4020517-4 gnd |
| topic_facet | Fonctions d'une variable réelle - Histoire Fonctions de variables réelles Geschichte Functions of real variables History Reelle Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002842958&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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