Abstract
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.
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References
A. Kolmogorov: Foundations of the Theory of Probability (Chelsea, New York 1950);
A. Kolmogorov Grundbegriffe der Wahrscheinlichkeitsrechnung (Springer, Berlin, Heidelberg, New York 1977)
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Additional Reading
Feller, W.: An Introduction to Probability Theory and Its Applications, Vol. I (Wiley, New York 1966)
Moran, P. A. P.: An Introduction to Probability Theory (Clarendon, Oxford 1968)
Parzen, E.: Modern Probability Theory and Its Applications (Wiley, New York 1966)
Reza, F.: An Introduction to Information Theory (McGraw-Hill, New York 1961)
Yu, F. T. S.: Optics and Information Theory (Wiley, New York 1976)
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© 1991 Springer-Verlag Berlin Heidelberg
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Frieden, B.R. (1991). The Axiomatic Approach. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97289-8_2
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DOI: https://doi.org/10.1007/978-3-642-97289-8_2
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