The mathematical basis of probability theory and continuum statistics

  • Ekkehart Kröner
Part of the International Centre for Mechanical Sciences book series (CISM, volume 92)


A. Kolmogorov develops the theory of probability starting from a small set of definitions and axioms from which the whole mathematical framework is derived. This is the usual manner in which also other mathematical (and physical) theories are constructed. As an example the group theory maybe mentioned.


Correlation Function Elementary Event Mathematical Basis Completeness Theorem Probability Density Functional 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. A.N. Kolmogorov, Foundations of the Theory of Probability, Chelsea Publishing Company, New York 1956MATHGoogle Scholar
  2. Yu.V. Prohorov and Yu.A. Rozanov, Probability Theory, Springer—Verlag, Berlin — Heidelberg — New York 1969CrossRefGoogle Scholar
  3. D. Morgenstern, Einfiihrung in die Wahrscheinlichkeitsrechnung und mathematische Statistik, Springer — Verlag, Berlin — Heidelberg — New York 1968CrossRefGoogle Scholar
  4. H. Cramér, Mathematical Methods of Statistics, Princeton Univer- sity Press, Princeton, N.J. 1946Google Scholar
  5. M. Loève, Probability Theory, Van Nostrand, Princeton, N.J. 1962Google Scholar
  6. B.W. Lindgren and G.W. McElrath, Introduction to Probability and Statistics, Macmillan Company, New York 1959 (elementary textbook)Google Scholar
  7. M.J. Beran, Statistical Continuum Theories, Interscience Publish ers, New York 1968MATHGoogle Scholar
  8. V. Volterra, Theory of Functionals and of Integral and Integro—Differential Equations, Dover, New York 1959MATHGoogle Scholar
  9. G. Evans, Functionals and Their Applications, Dover, New York 1964MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • Ekkehart Kröner
    • 1
  1. 1.University of StuttgartGermany

Personalised recommendations