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Associativity in a class of operations on spaces of distribution functions

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References

  1. Aczél, J.,Lectures on Functional Equations and Their Applications (Academic Press, New York, 1966).

    Google Scholar 

  2. Boas, R. P.,A Primer of Real Functions (The Math. Assoc. of Amer., New York, 1960).

    Google Scholar 

  3. Fréchet, M.,Sur les tableaux de corrélation dont les marges sont données, Ann. Univ. de LyonIII ser. fasc. 14A, 53–77 (1951).

    Google Scholar 

  4. Kemperman, J. H. B.,Product Measures for which Deviation and Minimum are Independent, Sankhya ser. A33, 271–288 (1971).

    Google Scholar 

  5. Ling, C. H.,Representation of Associative Functions, Publ. Math. Debrecen12, 189–212 (1965).

    Google Scholar 

  6. Loève, M.,Probability Theory (Van Nostrand, New York, 1963).

    Google Scholar 

  7. Mostert, P. S., andShields, A. L.,On the Structure of Semigroups on a Compact Manifold with Boundary, Ann. of Math.65, 117–143 (1957).

    Google Scholar 

  8. Schweizer, B.,Probabilistic Metric Spaces — the First 25 Years, The New York Statistician19, No.2, 3–6 (1967).

    Google Scholar 

  9. Schweizer, B.,Multiplications on the Space of Probability Distribution Functions, to appear in Aequationes Math.

  10. Schweizer, B. andSklar, A.,Associative Functions and Statistical Triangle Inequalities, Publ. Math. Debrecen8, 169–186 (1961).

    Google Scholar 

  11. Schweizer, B. andSklar, A.,Associative Functions and Abstract Semigroups, Publ. Math. Debrecen10, 69–81 (1963).

    Google Scholar 

  12. Schweizer, B. andSklar, A.,Mesures aléatoires de l'information, C. R. Acad. Sc. Paris269, sérieA, 721–723 (1969).

    Google Scholar 

  13. Schweizer, B. andSklar, A.,Mesure aléatoire de l'information et mesure de l'information par un ensemble d'observateurs, C. R. Acad. Sc. Paris272, sérieA, 149–152 (1971).

    Google Scholar 

  14. Schweizer, B. andSklar, A.,Operations on Distribution Functions Not Derivable from Operations on Random Variables, to appear in Studia Math.

  15. Serstnev, A. N.,On a Probabilistic Generalization of Metric Spaces (Russian), Uch. Zap, Kazan Gos. Univ.124, Book2, 3–11 (1964).

    Google Scholar 

  16. Sklar, A.,Fonctions de repartition a n dimensions et leur marges, Publ. Inst. Statistique Univ. ParisVIII, 229–231 (1959.

    Google Scholar 

  17. Sklar, A.,Random Variables, Joint Distribution Functions and Copulas, to appear in Kybernetika.

Download references

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This work is taken from the author's doctoral thesis, written under the thoughtful direction of Professor Abe Sklar at the Illinois Institute of Technology. The author is especially grateful to Professor Berthold Schweizer for suggesting many improvements in the original manuscript.

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Frank, M.J. Associativity in a class of operations on spaces of distribution functions. Aeq. Math. 12, 121–144 (1975). https://doi.org/10.1007/BF01836543

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