ERGODIC PROBLEM IN QUANTITATIVE LANGUAGE

Shiro Ishikawa (Japan)

Received October 25, 2008

References:

[1] Augustine (St.). Confessions, F. J. Sheed (translator), Hackett, Indiapolis/ Cambridge, 1993. [2] R. Carnap, Beobacthungssprache und theoretische Sprache, Dialectica, XII, 1958 (English translation “Observation Language and Theoretical Language” Rudolf Carnap, Logical Empiricist, D. Reidel Publishing Company, Dordrecht, Holl., 1975). [3] E. B. Davies, Quantum Theory of Open Systems, Academic Press, New York, 1976. [4] D. Hume, Treatise of Human Nature, E. C. Mossener, ed., Viking Press, 1986. [5] S. Ishikawa, Fuzzy inferences by algebraic method, Fuzzy Sets Systems 87 (1997), 181-200. [6] S. Ishikawa, A dynamical system theoretical approach to equilibrium statistical mechanics, Far East J. Dyn. Syst. 3(1) (2001), 9-28. [7] S. Ishikawa, Mathematical Foundations of Measurement Theory, Keio University Press Inc., 2006, pp. 335. (The PDF-version of this book can be seen at http://www.keio-up.co.jp/kup/mfomt/). [8] S. Ishikawa, A new formulation of measurement theory, Far East J. Dyn. Syst. 10(1) (2008), 107-117. [9] S. Ishikawa, Dynamical systems, measurements, quantitative languages and Zeno’s paradoxes, Far East J. Dyn. Syst. 10(3) (2008), 277-292. [10] S. Ishikawa, K. Kikuchi and M. Nakamura, Elementary school mathematics in quantitative language, Far East J. Math. Edu. 2(2) (2008), 165-180. [11] A. Kolmogorov, Foundations of Probability (Translation), Chelsea Publishing Co., 1950. [12] U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin, New York, 1985. [13] D. Ruelle, Statistical Mechanics, Rigorous Results, W. A. Benjamin Inc., New York-Amsterdam, 1969. [14] S. Sakai, -algebras and -algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York, 1971. [15] Ferdinand de Saussure, Course in General Linguistics, Charles Bally and Albert Sechehaye, eds., Trans. Roy Harris, Open Court, La Salle, Illinois, 1983. [16] J. von Neumann, Mathematical Foundations of Quantum Mechanics, Springer-Verlag, 1932. [17] L. Wittgenstein, Philosophical Investigations, Prentice Hall, 3rd ed., 1973.

Keywords and phrases: measurement theory, quantitative language, equilibrium statistical mechanics, ergodic hypothesis, probability.