## Browse content

### Table of contents

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#### Chapter 1 - Introduction

Pages 1-37 - Book chapterAbstract only
#### Chapter 2 - Construction of Numerical Functions

Pages 38-70 - Book chapterAbstract only
#### Chapter 3 - Extensive Measurement

Pages 71-135 - Book chapterAbstract only
#### Chapter 4 - Difference Measurement

Pages 136-198 - Book chapterAbstract only
#### Chapter 5 - Probability Representations

Pages 199-244 - Book chapterAbstract only
#### Chapter 6 - Additive Conjoint Measurement

Pages 245-315 - Book chapterAbstract only
#### Chapter 7 - Polynomial Conjoint Measurement

Pages 316-368 - Book chapterAbstract only
#### Chapter 8 - Conditional Expected Utility

Pages 369-422 - Book chapterAbstract only
#### Chapter 9 - Measurement Inequalities

Pages 423-453 - Book chapterAbstract only
#### Chapter 10 - Dimensional Analysis and Numerical Laws

Pages 454-544 - Book chapterNo access
#### Answers and Hints to Selected Exercises

Pages 545-550 - Book chapterNo access
#### References

Pages 551-569 - Book chapterNo access
#### Author Index

Pages 571-575 - Book chapterNo access
#### Subject Index

Pages 577-584

## About the book

### Description

Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utilization of constructive methods, and as a series of isomorphism theorems leading to consistent numerical solutions. The text also explains the counting of units in relation to an empirical relational structure which contains a concatenation operation. The book notes some special variants which arise in connection with relativity and thermodynamics. The text cites examples from physics and psychology for which additive conjoint measurement provides a possible method of fundamental measurement. The book will greatly benefit mathematicians, econometricians, and academicians in advanced mathematics or physics.

Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utilization of constructive methods, and as a series of isomorphism theorems leading to consistent numerical solutions. The text also explains the counting of units in relation to an empirical relational structure which contains a concatenation operation. The book notes some special variants which arise in connection with relativity and thermodynamics. The text cites examples from physics and psychology for which additive conjoint measurement provides a possible method of fundamental measurement. The book will greatly benefit mathematicians, econometricians, and academicians in advanced mathematics or physics.

## Details

### ISBN

978-0-12-425401-5

### Language

English

### Published

1971

### Copyright

Copyright © 1971 Elsevier Inc. All rights reserved.

### Imprint

Academic Press