The Axiomatic Approach

  • B. Roy Frieden
Part of the Springer Series in Information Sciences book series (SSINF, volume 10)


The entire edifice of probability theory, and its offshoots statistics and stochastic processes, rests upon three famous axioms of Kolmogoroff [2.1]. Indeed, everything in this book derives from these simple axioms. The axioms are deceptively simple, in fact so simple that at first they appear to say nothing at all. However, let us recall that axioms are supposed to be that way. The simpler they appear, and the more they imply, the better they are mathematically.


Conditional Probability Point Spread Function Event Space Object Plane Axiomatic Approach 
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  1. 2.1
    A. Kolmogorov: Foundations of the Theory of Probability (Chelsea, New York 1950);Google Scholar
  2. 2.1a
    A. Kolmogorov Grundbegriffe der Wahrscheinlichkeitsrechnung (Springer, Berlin, Heidelberg, New York 1977)Google Scholar
  3. 2.2
    A. Papoulis: Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York 1965)MATHGoogle Scholar
  4. 2.3
    C. E. Shannon: Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)MathSciNetMATHGoogle Scholar
  5. 2.4
    R. A. Fisher: Proc. Cambridge Philos. Soc. 22, 700–725 (1925)ADSMATHCrossRefGoogle Scholar
  6. 2.5
    R. V. L. Hartley: Bell Syst. Tech. J. 7, 535 (1928)Google Scholar
  7. 2.6
    W. H. Richardson: J Opt. Soc. Am. 62, 55–59 (1972)ADSCrossRefGoogle Scholar
  8. 2.7
    R. A. Howard: Dynamic Probability Systems (Wiley, New York 1971)Google Scholar

Additional Reading

  1. Feller, W.: An Introduction to Probability Theory and Its Applications, Vol. I (Wiley, New York 1966)Google Scholar
  2. Moran, P. A. P.: An Introduction to Probability Theory (Clarendon, Oxford 1968)MATHGoogle Scholar
  3. Parzen, E.: Modern Probability Theory and Its Applications (Wiley, New York 1966)Google Scholar
  4. Reza, F.: An Introduction to Information Theory (McGraw-Hill, New York 1961)Google Scholar
  5. Yu, F. T. S.: Optics and Information Theory (Wiley, New York 1976)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • B. Roy Frieden
    • 1
  1. 1.Optical Sciences CenterThe University of ArizonaTucsonUSA

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