A NEW FORMULATION OF MEASUREMENT THEORY

Shiro Ishikawa (Japan)

Received November 24, 2007

References:

[1] E. B. Davies, Quantum Theory of Open Systems, Academic Press, 1976. [2] S. Ishikawa, Fuzzy inferences by algebraic method, Fuzzy Sets and Systems 87 (1997), 181-200. [3] S. Ishikawa, T. Arai and T. Takamura, A dynamical system theoretical approach to Newtonian mechanics, Far East J. Dynamical Systems 1 (1999), 1-34. [4] S. Ishikawa, Mathematical Foundations of Measurement Theory, Keio University Press Inc., 2006. (The PDF-version of this book can be seen at http://www.keio-up.co.jp/kup/mfomt). [5] I. Kant, Critique of Pure Reason, (1781), Cambridge Edition of the Works of Immanuel Kant, Translators: Paul Guyer, Allen W. Wood, 1998. [6] E. Prugovečki, Quantum Mechanics in Hilbert Space, Academic Press, 1981. [7] S. Sakai, -algebras and -algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, 1971. [8] J. von Neumann, Mathematical Foundations of Quantum Mechanics, Springer-Verlag, 1932.

Keywords and phrases: measurement, mechanical world view, dynamical system theory, quantum mechanics, probability.