References
Aczél, J.,Lectures on Functional Equations and Their Applications (Academic Press, New York, 1966).
Boas, R. P.,A Primer of Real Functions (The Math. Assoc. of Amer., New York, 1960).
Fréchet, M.,Sur les tableaux de corrélation dont les marges sont données, Ann. Univ. de LyonIII ser. fasc. 14A, 53–77 (1951).
Kemperman, J. H. B.,Product Measures for which Deviation and Minimum are Independent, Sankhya ser. A33, 271–288 (1971).
Ling, C. H.,Representation of Associative Functions, Publ. Math. Debrecen12, 189–212 (1965).
Loève, M.,Probability Theory (Van Nostrand, New York, 1963).
Mostert, P. S., andShields, A. L.,On the Structure of Semigroups on a Compact Manifold with Boundary, Ann. of Math.65, 117–143 (1957).
Schweizer, B.,Probabilistic Metric Spaces — the First 25 Years, The New York Statistician19, No.2, 3–6 (1967).
Schweizer, B.,Multiplications on the Space of Probability Distribution Functions, to appear in Aequationes Math.
Schweizer, B. andSklar, A.,Associative Functions and Statistical Triangle Inequalities, Publ. Math. Debrecen8, 169–186 (1961).
Schweizer, B. andSklar, A.,Associative Functions and Abstract Semigroups, Publ. Math. Debrecen10, 69–81 (1963).
Schweizer, B. andSklar, A.,Mesures aléatoires de l'information, C. R. Acad. Sc. Paris269, sérieA, 721–723 (1969).
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).
Schweizer, B. andSklar, A.,Operations on Distribution Functions Not Derivable from Operations on Random Variables, to appear in Studia Math.
Serstnev, A. N.,On a Probabilistic Generalization of Metric Spaces (Russian), Uch. Zap, Kazan Gos. Univ.124, Book2, 3–11 (1964).
Sklar, A.,Fonctions de repartition a n dimensions et leur marges, Publ. Inst. Statistique Univ. ParisVIII, 229–231 (1959.
Sklar, A.,Random Variables, Joint Distribution Functions and Copulas, to appear in Kybernetika.
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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.