Additive and Polynomial Representations

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Academic Press, May 12, 2014 - Science - 608 pages
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.
 

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Contents

Chapter 1 Introduction
1
Chapter 2 Construction of Numerical Functions
38
Chapter 3 Extensive Measurement
71
Chapter 4 Difference Measurement
136
Chapter 5 Probability Representations
199
Chapter 6 Additive Conjoint Measurement
245
Chapter 7 Polynomial Conjoint Measurement
316
Chapter 8 Conditional Expected Utility
369
Chapter g Measurement Inequalities
423
Chapter l0 Dimensional Analysis and Numerical Laws
454
Answers and Hints to Selected Exercises
545
References
551
Author Index
571
Subject Index
577
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