Abstract measurement theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass. [u.a.]
MIT Press
1985
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 334 S. |
| ISBN: | 0262140373 |
Internformat
MARC
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| 245 | 1 | 0 | |a Abstract measurement theory |c Louis Narens |
| 264 | 1 | |a Cambridge, Mass. [u.a.] |b MIT Press |c 1985 | |
| 300 | |a VII, 334 S. | ||
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Datensatz im Suchindex
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| adam_text | Contents
1 Introduction 1
1 Introduction 1
2 Organization of the Book 9
3 Preliminary Definitions and Conventions 12
a. Set theory 12
b. Relational structures 13
c. Ordering relations 15
d. Algebraic structures 17
1 ORDERED STRUCTURES 21
2 Scale Types and Positive Concatenation Structures 23
1 Introduction and Holder s Theorem 23
2 Ordinal Structures 31
3 Monotonic Structures 39
4 Scalar Structures 42
5 Linear Structures 53
6 Other Scale Types and a Discussion 64
a. Absolute scales 64
b. The impossibility of relational structures of order type 6
satisfying n point homogeneity and « point uniqueness
for n 2 65
c. A discussion 67
d. Structures with invariant elements 69
e. A remark about homogeneity and axiomatizability 72
7 Positive Concatenation Structures 73
8 Extensive Measurement 78
a. Introduction 78
b. Extensive structures 78
c. Nonadditive representations 84
d. Weber s law structures 88
e. Qualitative probability (as extensive measurement) 94
f. Qualitative stochastic independence 97
vi Contents
9 Automorphisms of Positive Concatenation Structures 102
10 Fundamental Unit Structures 110
11 Smooth Positive Concatenation Structures 126
12 Extensions of Pre Unit Structures 139
13 Dedekind Completions of Positive Concatenation
Structures 146
14 Positive Concatenation Structures and Meaningfulness 155
15 Intensive Structures 171
16 Historical Note 177
3 Ordered Conjoint Structures 182
1 Introduction 182
2 aZ Solvable Structures 183
3 Nonnegative ai Conjoint Structures 194
4 The Thomsen Condition and Additivity 201
a. Overview 201
b. Additive representations 201
c. Multiplicative representations 208
d. Component in variance 209
e. Bisymmetric structures 210
f. Other conditions for additivity 213
5 Distributive Structures 214
a. Introduction 214
b. Distributive operations 214
c. Multiplicative scalar representations 216
d. Some examples of distributive operations 224
e. The set of translations 9~ 226
f. Weber s law for conjoint structures 231
6 Velocity Structures 232
7 Historical Note 237
Contents vii
II AXIOMATIZABILITY AND NON ARCHIMEDEAN
STRUCTURES 241
4 Ordered Field Extensions of the Reals 243
1 Introduction 243
2 Reduced Powers of the Reals 243
3 Ultrafilters 246
4 Ultrapowers of the Reals 249
5 Ordered Field Extensions of the Reals 253
6 2 Valued Measures 256
7 Re*, ^Representations 258
8 Historical Note 259
5 Non Archimedean Additive Structures 261
1 Introduction 261
2 Additive Conjoint Structures 262
3 Additive Concatenation Structures 273
4 Qualitative Probability 282
5 Historical Note 293
6 tos s Theorem 294
1 Introduction 294
2 First Order Languages 295
3 Models of First Order Languages 296
4 Los s Theorem 300
5 Nonstandard Analysis 303
6 The Downward Lowenheim Skolem Theorem 313
7 The Compactness Theorem 316
8 Nonaxiomatizability of Certain Classes of Qualitative
Probability Structures 321
9 Historical Note 326
References 327
Index 331
|
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| id | DE-604.BV000344102 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:12:39Z |
| institution | BVB |
| isbn | 0262140373 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000213814 |
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| physical | VII, 334 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | MIT Press |
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| spelling | Narens, Louis Verfasser (DE-588)1084236524 aut Abstract measurement theory Louis Narens Cambridge, Mass. [u.a.] MIT Press 1985 VII, 334 S. txt rdacontent n rdamedia nc rdacarrier Maßtheorie (DE-588)4074626-4 gnd rswk-swf Messtheorie (DE-588)4169537-9 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 Messtheorie (DE-588)4169537-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000213814&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Narens, Louis Abstract measurement theory Maßtheorie (DE-588)4074626-4 gnd Messtheorie (DE-588)4169537-9 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4169537-9 |
| title | Abstract measurement theory |
| title_auth | Abstract measurement theory |
| title_exact_search | Abstract measurement theory |
| title_full | Abstract measurement theory Louis Narens |
| title_fullStr | Abstract measurement theory Louis Narens |
| title_full_unstemmed | Abstract measurement theory Louis Narens |
| title_short | Abstract measurement theory |
| title_sort | abstract measurement theory |
| topic | Maßtheorie (DE-588)4074626-4 gnd Messtheorie (DE-588)4169537-9 gnd |
| topic_facet | Maßtheorie Messtheorie |
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