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| MATHEMATICAL FOUNDATIONS OF MEASUREMENT THEORY |
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The mathematical foundations of measurement theory will be proposed in this book. As it is usually said that there is no science without measurement , the concept of "measurement" is certainly the most fundamental in science. In this book, the measurement theory ( proposed by the author recently) is comprehensively introduced to graduate students chiefly. The measurement theory has several aspects, that is, 1.the mathematical representation of "the mechanical world view" 2.the axiomatic formulation of system theory and statistics 3.the algebraic abstraction of quantum mechanics 4.the most fundamental theory of engineering 5.the mathematical representation of philosophical epistemology In the most part of this book, the above 2. and 3. are mainly and mathematically treated. All people that are involved in science may be recommended to read this book. 
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Title MATHEMATICAL FOUNDATIONS OF MEASUREMENT THEORY Author Shiro ISHIKAWA (Associated professor) Department of mathematics, Faculty of science and technology, Keio University 3-14-1, Hiyoshi, Kohoku-ku, YOKOHAMA 223-8522 JAPAN (For the precise contents, see the above sample PDF file) Chap. 1 The philosophy of measurement theory Chap. 2 Measurements (mathematical preparations, Axiom 1, frequency probability) Chap. 3 The relation among systems (Newtonian equation, Schrodinger equation Axiom 2, measurability theorem) Chap. 4 Boltzmann's equilibrium statistical mechanics (ergodic hypothesis ) Chap. 5 Fisher's statistics I (maximum likelihood method, testingt statistical hypothesis) Chap. 6 Fisher's statistics II (regression analysis) Chap. 7 Practical logic (syllogism) Chap. 8 Statistical measurements in C*-algebraic formulation (Bayes theorem, Kalman filter, entropy, belief measurement (subjective Bayes statistics)) Chap. 9 Statistical measurements in W*-algebraic formulation (quantum mechanics, moment method) Chap.10 Newtonian mechanics in measurement theory(measurement theoretical Kolmogorov's extension theorem, the definition of "trajectory", Brownian motion) Chap.11 Measurement error (random measurement, the principle of equal probability) Chap.12 Heisenberg's uncertainty relation EPR-paradox ,uncertainty relation |
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