Abstract
In pr. theory, a distribution junction (d.f.), to be denoted by F, with or without affixes, is a nondecreasing function, continuous from the left and bounded by 0 and 1 on R.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Alexandrov, A. D. Additive set functions in abstract spaces. Matern. Sbornik 8, 9, 13 (1940, 1941, 1943).
Billingsley, P. Weak convergence of measures: applications in probability. Soc. Indust. and Appl. Math. (1971).
Bochner, S. Monotone Funktionen, Stieltjes Integrale, und harmonische Analyse. Math. Ann. 108 (1933).
Bray, H. E. Elementary properties of the Stieltjes Integral. Ann. Math. 20 (1919).
Dugué, D. Analyticité et convexité des fonctions caractéristiques. Ann. Inst. H. Poincaré XXII (1952).
Fortet, R. Calcul des moments d’une fonction de repartition à partir de sa characteristic. Bull. Sc. Math. 88 (1944).
Fréchet, M. and Shohat, J. A proof of the generalized second limit theorem in the theory of probability. Trans. Am. Math. Soc. 33 (1931).
Helly, E. Ueber lineare Funktionaloperationen. Sitz. Nat. Kais. Akad. Wiss. 121 (1949).
Kawata, T. and Udagawa, M. On infinite convolutions. Kadai Math. Sem. 3 (1949).
Le Cam. Convergence in distribution of stochastic processes. Univ. Cal. Publ. Stat. 2, no 4 (1957).
Marcienkiewicz. Sur les fonctions indépendantes. Fund. Math. 31 (1939).
Marcienkiewicz. Sur une propriété de la loi de Gauss. Math. Zeit. 44 (1939).
Parzen, E. On uniform convergence of families of sequences of random variables. Univ. Calif. Publ. Stat. 2 (1954).
Polya, G. Remark on characteristic functions. Proc. First Berkeley Symp. on Stat, and Prob. (1949).
Prohorov, U. V. Convergence of random processes and limit theorems of probability theory in Russia. Teoria Veroyatnostey, 1 (1956).
Zygmund, A. A remark on characteristic functions. Ann. Math. Stat. 18 (1947).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1977 Springer-Verlag Inc.
About this chapter
Cite this chapter
Loève, M. (1977). Distribution Functions and Characteristic Functions. In: Probability Theory I. Graduate Texts in Mathematics, vol 45. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9464-8_5
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9464-8_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9466-2
Online ISBN: 978-1-4684-9464-8
eBook Packages: Springer Book Archive