Advertisement

Lecture Notes on Concepts and Measures of Information

  • Hans W. Gottinger
Part of the International Centre for Mechanical Sciences book series (CISM, volume 219)

Abstract

In recent years a considerable amount of work has been done on concepts and measures of information within and beyond the fields of engineering and mathematics.

Keywords

Boolean Algebra Semantic Information Risk Function Qualitative Information Information Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kolmogorov,A.N., ‘Three Approaches to the Definition of the Concept “Quantity of Information”’, Problemy Peredaci Informacii 1, 1965, 3 (in Russian)MATHMathSciNetGoogle Scholar
  2. 2.
    Kolmogorov, A.N., ‘Logical Basis for Information Theory and Probability Theory’, IEEE Trans. Information Theory IT-14, 1967, 662Google Scholar
  3. 3.
    Gottinger, H.W., ‘Qualitative Information and Compara- tive Informativeness’, Kybernetik 13, 1973, 81CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Gottinger, H.W., ‘Konstruktion subjektiver Wahrschein- lichkeiten’, Math. Operationsforschung u.Statist. 5, 1974, 50MathSciNetGoogle Scholar
  5. 5.
    Blackwell, D., ‘Comparison of Experiments’, Proc.2nd Berkeley Symp.Math. Statist. and Probability, 1953, 93Google Scholar
  6. 6.
    Blackwell, D., Girshick,M.A., Theory of Games and Sta- tistical Decisions, Wiley: New York 1954Google Scholar
  7. 7.
    Shannon, C.E., Weaver, W., The Mathematical Theory of Communication, Illinois Uni.Press: Urbana, Ill. 1949MATHGoogle Scholar
  8. 8.
    Wiener, N., Cybernetics, M.I.T. Press: Cambridge(Mass. ) 1948Google Scholar
  9. 9.
    Fadeev, D.K., ‘On the Concept of the Entropy for a Finite Probability Model’, Uspehi Mat. Nauk 11, 1958, 227 (in Russian)Google Scholar
  10. 10.
    Erdös, P., ‘On the Distribution Function of Additive Functions’’, Ann. of Math. 47, 1946, 1CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    MacKay, D.M., Information, Mechanism and Meaning,M.I.T. Press: Cambridge, 1969Google Scholar
  12. 12.
    Rényi, A., ‘On Measures of Entropy and Information’, Proc. 4th Berkeley Symp.Math. Statist. and Probability, 1961, 547Google Scholar
  13. 13.
    Kelly, J.L., ‘A new Interpretation of Information Rate’, Bell System Technical Jour. 35, 1956, 917CrossRefGoogle Scholar
  14. 14.
    Khinchin, A.I., Mathematical Foundations of Information Theory, Dover Pubi.: New York 1957MATHGoogle Scholar
  15. 15.
    Tveberg, H., ‘A New Derivation of the Information Function’, Math. Scand. 6, 1958, 297MathSciNetGoogle Scholar
  16. 16.
    Kendall, D.G., ‘Functional Equations in Information Theory’, Zeitschr. Wahrscheinlichkeitstheorie 2, 1964, 225CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Lee, P.M., ‘On the Axioms of Information Theory’, Ann. Math. Statist. 35, 1964, 415CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Gottinger, H.W., ‘Review of Concepts and Theories of Probability’, Scientia (Rivista di Scienza), 109, 1974, 83MathSciNetGoogle Scholar
  19. 19.
    Bar-Hillel, Y. and Carnap R., ‘An Outline of a Theory of Semantic Information’, Tech.Rep.No.247, Research Lab. of Electronics, M.I.T. 1952, in Language and Information, Bar-Hillel,Y. ed.,Addison-Wesley, Reading, Mass. 1964, 221Google Scholar
  20. 20.
    Jeffreys, H.,Theory of Probability, 3rd ed., Clarendon Press: Oxford 1961Google Scholar
  21. 21.
    Heerden van, P.J., ’The Foundation of Empirical Knowledge’, Uitgeverij Wistik, Wassenaar, Holland 1968Google Scholar
  22. 22.
    Ingarden,R.S. and Urbanik,K., ‘Information without Probability’, Colloq.Math. 9, 1962, 131Google Scholar
  23. 23.
    Ingarden, R.S., ‘A Simplified Axiomatic Definition of Information’, Bull.Acad.Sci. Polonaise, Ser. math.,astr. et phys., 11, 1963, 209MathSciNetGoogle Scholar
  24. 24.
    Ingarden, R.S., ‘Simplified Axioms for Information without Probability’, Prace Matematyczne 9, 1965, 273MATHMathSciNetGoogle Scholar
  25. 25.
    Rényi, A., Wahrscheinlichkeitsrechnung (mit einem Anhang fiber Informationstheorie), VEB Deutscher Verlag der Wissenschaften: Berlin 1962Google Scholar
  26. 26.
    Rénvi, A., ‘On the Foundations of Information Theory’, Bull. International Statistical Institute 33, 1965Google Scholar
  27. 27.
    Kampé de Fériet, J., ‘Mesure de l’information fournie par un évènement’, Les Probabilités sur les Structures Algébriaues, Paris: Symp. CNRS, 1970, 191Google Scholar
  28. 28.
    Fuchs, L., Partially Ordered Algebraic Systems, Pergamon: London 1963MATHGoogle Scholar
  29. 29.
    Sikorski, R., Boolean Algebras, ( 2nd ed. ), Springer, Ceöttingen-Berlin 1964MATHGoogle Scholar
  30. 30.
    Gottinger, H.W., ‘Konstruktion subjektiver Wahrscheinlichkeiten’, Math. Operationsforschung u.Statist.5, 1974, 509Google Scholar
  31. 31.
    Domotor, Z., ‘Probabilistic Relational Structures and Applications’, Tech. Report 144, Inst. Math. Studies Social Sciences, Stanford University, 1969Google Scholar
  32. 32.
    Ore, O., ‘Theory of Equivalence Relations’, Duke Mathematical Jour, 9, 1942, 573CrossRefMATHMathSciNetGoogle Scholar
  33. 33.
    Maeda, S., ‘A Lattice-Theoretic Treatment of Stochastic Independence’, Jour.Sci.Hiroshima Univ. 27, 1963,Ser.A-1,1Google Scholar
  34. 34.
    Scott, D., ‘Measurement Structures and Linear Inequalities’, Jour. Math. Psychology 1, 1964, 233CrossRefMATHGoogle Scholar
  35. 35.
    Wells, R., ‘A Measure of Subjective Information’, Proc. Symp.Appl. Math.(Amer. Math. Soc.) 12, 1961, 237Google Scholar
  36. 36.
    Csâszar, A., Foundations of General Topology, Pergamon, London 1963Google Scholar
  37. 37.
    Horn, A. and Tarski, A.,’Measures in Boolean Algebras’, Trans. Amer. Math. Soc. 64 1948, 467CrossRefMATHMathSciNetGoogle Scholar
  38. 38.
    Kelley, J.L., ‘Measures in Boolean Algebras’, Pacific Jour. Math. 9, 1959, 1165MATHMathSciNetGoogle Scholar
  39. 39.
    Kappos, D.A., Strukturtheorie der Wahrscheinlichkeitsfelder und -räume, Springer: Berlin 1960CrossRefGoogle Scholar
  40. 40.
    Groot de, M., ‘Uncertainty, Information and Sequential Experiments’, Ann. Math. Statist. 33, 1962, 404CrossRefMathSciNetGoogle Scholar
  41. 41.
    Groot de, M., ’Optimal Statistical Decisions; McGraw-Hill: New York 1970Google Scholar
  42. 42.
    Birnbaum, A., ‘On the Foundations of Statistical Inference’, Ann. Math. Statist. 32, 1961, 414CrossRefMATHMathSciNetGoogle Scholar
  43. 43.
    McGuire,C.B., ‘Comparison of Information Structures’, in Decision and Organization, Radner, R. and McGuire, C.B. eds., North Holland,Amsterdam 1972, 101Google Scholar
  44. 44.
    Gottinger, H.W., ‘Some Measures of Information arising in Statistical Games’, Kybernetik 15, 1974, 111CrossRefMATHMathSciNetGoogle Scholar
  45. 45.
    Groot de, M.,Optimal Statistical Decisions; McGraw-Hill: New York 1970Google Scholar
  46. 46.
    Howard, R.A.,’Information Value Theory’, IEEE Trans.Syst. Science and Cyber. SSC-2, 1966, 22Google Scholar
  47. 47.
    Marschak, J., ‘Economics of Information Systems’, in Frontiers of Quantitative Economics,Intrilligator, M.D. ed., North-Holland, Amsterdam 1971, 31Google Scholar
  48. 48.
    Marschak, J. and Radner, R., Economic Theory of Teams, Yale Univ.Press, New Haven 1972MATHGoogle Scholar
  49. 49.
    Belis, M. and Guiasu, S., ‘A Quantitative-Qualitative Measure of Information in Cybernetic Systems’, IEEE Trans. Information Theory IT-14, 1967, 593Google Scholar
  50. 50.
    Guiasu, S., Mathematical Structure of Finite Random Cybernetic Systems, CISM Courses and Lectures No. 86, Wien: Springer-Verlag 1971Google Scholar
  51. 51.
    Longo, G., Quantitative-Qualitative Measure of Information, CISM Courses and Lectures No. 138, Wien: SpringerVerlag 1972Google Scholar
  52. 52.
    Marschak, J., ‘Optimal Systems for Information and Decision’, Techniques of Optimization, Academic Press: New York 1972, 355Google Scholar
  53. 53.
    Marschak, J., ‘Limited Role of Entropy in Information Economics’, in 5th Conference on Optimization Techniques, Part II, Conti, R. et al. eds., Springer, New York 1973, 264Google Scholar
  54. 54.
    Marschak, J., ‘Value and Cost of Information Systems’, Working Paper 51, Wirtschaftstheoretische Abt., Universität Bonn, September 1973Google Scholar
  55. 55.
    Gottinger, H.W., ‘Computable Organizations - Representation by Sequential Machine Theory’, Ann. Systems Research 3, 1973, 81MathSciNetGoogle Scholar
  56. 56.
    Gottinger, H.W., ‘Information Structures in Dynamic Team Decision Problems’, to appear in Economic Computation and Economic Cybernetic Studies and Research (Bucharest), 1975.Google Scholar

Copyright information

© Springer-Verlag Wien 1975

Authors and Affiliations

  • Hans W. Gottinger
    • 1
  1. 1.University of BielefeldF.R. of Germany

Personalised recommendations