ε-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms
Annales de l'I.H.P. Probabilités et statistiques, Tome 9 (1973) no. 2, p. 113-144
@article{AIHPB_1973__9_2_113_0,
     author = {Gauglhofer, Margrit and Bharucha-Reid, A. T.},
     title = {$\varepsilon $-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {9},
     number = {2},
     year = {1973},
     pages = {113-144},
     zbl = {0261.60011},
     language = {en},
     url = {http://http://www.numdam.org/item/AIHPB_1973__9_2_113_0}
}
Gauglhofer, Margrit; Bharucha-Reid, A. T. $\varepsilon $-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms. Annales de l'I.H.P. Probabilités et statistiques, Tome 9 (1973) no. 2, pp. 113-144. http://www.numdam.org/item/AIHPB_1973__9_2_113_0/

[1] R. Adler, A. Konheim and M. Mcandrew, Topological entropy. Trans. Amer. Math. Soc., t. 11, 1965, p. 309-319. | MR 175106 | Zbl 0127.13102

[2] S. Chevet, p-ellipsoides de lp; mesures cylindriques gaussiennes. Les probabilités sur les structures algébriques, p. 55-73. Centre National de la Recherche Scientifique, Paris, 1970. | MR 410878 | Zbl 0244.46010

[3] S. Chevet, A. Badrikian and P. Bernard, Application de la notion d'∈-entropie à la recherche de conditions d'existence de modifications continues de fonctions aléatoires. Les probabilités sur les structures algébriques, p. 33-41. Centre National de la Recherche Scientifique, Paris, 1970. | MR 348808 | Zbl 0248.60035

[4] K.L. Chung, A Course in Probability Theory, Harcourt, Brace and World, New York, 1968. | MR 229268 | Zbl 0159.45701

[5] E.I. Dinaburg, The relation between topological entropy and metric entropy (Russian). Dokl. Acad. Nauk SSSR, t. 190, 1970, p. 19-22. | MR 255765 | Zbl 0196.26401

[6] R.M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Functional Analysis, t. 1, 1967, p. 290-330. | MR 220340 | Zbl 0188.20502

[7] R.M. Dudley, Some uses of ∈-entropy in probability theory. Les probabilités sur les structures algébriques, p. 113-122, Centre National de la Recherche Scientifique, Paris, 1970. | MR 410879 | Zbl 0231.60029

[8] R.M. Dudley, Small operators between Banach and Hilbert spaces. Studia Math., t. 38, 1970, p. 35-41. | MR 275193 | Zbl 0205.43101

[9] J. Dugundji, Topology. Allyn and Bacon, Boston, 1965. | MR 478089 | Zbl 0144.21501

[10] V.D. Erohin, Asymptotic theory of the ∈-entropy of analytic functions (Russian). Dokl. Akad. Nauk SSSR, t. 120, 1958, p. 949-952. | MR 102744 | Zbl 0098.08701

[11] B.V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (Translated from the Russian), Addison-Wesley, Reading, Mass., 1954. | MR 62975 | Zbl 0056.36001

[12] L.W. Goodwyn, Topological entropy bounds measure-theoretic entropy. Proc. Amer. Math. Soc., t. 23, 1969, p. 679-688. | MR 247030 | Zbl 0186.09804

[13] A.I. Khinchin, Mathematical Foundations of Information Theory (Translated from the Russian), Dover, New York, 1957. | MR 92709 | Zbl 0088.10404

[14] A.N. Kolmogorov, On the representation of continuous functions of several variables by superposition of continuous functions of a smaller number of variables (Russian). Dokl. Akad. Nauk SSSR, t. 108, 1956, p. 179-182. | MR 80129 | Zbl 0128.27803

[15] A.N. Kolmogorov and V.M. Tihomirov, ∈-entropy and ∈-capacity of sets in function spaces (Translated from the Russian). A. M. S. Translations, série 2, t. 17, 1961, p. 277-364. | MR 124720 | Zbl 0133.06703

[16] M. Loève, Probability Theory, Third Ed., Van Nostrand, Princeton, N. J., 1963. | MR 203748 | Zbl 0108.14202

[17] G.G. Lorentz, Approximation of Functions. Holt, Rinehart and Winston, New York, 1966. | MR 213785 | Zbl 0153.38901

[18] G.G. Lorentz, Metric entropy and approximation. Bull. Amer. Math. Soc., t. 72, 1966, p. 903-937. | MR 203320 | Zbl 0158.13603

[19] E. Lukacs, Characteristic Functions, Griffin, London, 1960. | MR 124075 | Zbl 0087.33605

[20] E.C. Posner and E.R. Rodemich, Epsilon entropy and data compression. Ann. Math. Statist., t. 42, 1971, p. 2079-2125. | MR 297458 | Zbl 0232.94007

[21] R.T. Prosser, The ∈-entropy and ∈-capacity of certain time-varying channels. J. Math. Anal. Appl., t. 16, 1966, p. 553-573. | MR 205750 | Zbl 0161.38702

[22] R.T. Prosser, On the analysis and synthesis of certain abstract systems. Bull. Amer. Math. Soc., t. 77, 1971, p. 444-448. | MR 274094 | Zbl 0213.49602

[23] A. Rényi, Probability Theory. North-Holland, Amsterdam, 1970. | MR 315747 | Zbl 0206.18002

[24] J. Riordan, Introduction to Combinatorial Analysis. Wiley, New York, 1958. | MR 96594 | Zbl 0078.00805

[25] J. Riordan, Combinatorial Identities. Wiley, New York, 1968. | MR 231725 | Zbl 0194.00502

[26] V. Strassen and R.M. Dudley, The central limit theorem and ∈-entropy. Lecture Notes in Mathematics, vol. 89.Probability and Information Theory, p. 224-231. Springer-Verlag, Berlin, 1969. | MR 279872 | Zbl 0196.21101

[27] V.N. Sudakov, Gaussian measures, Cauchy measures and ∈-entropy (Russian). Dokl. Akad. Nauk SSSR, t. 185, 1969, p. 51-53. | MR 247034 | Zbl 0224.60018

[28] A.G. Vituškin, On Hilbert's thirteenth problem (Russian). Dokl. Akad. Nauk SSSR, t. 95, 1954, p. 701-704. | MR 62212

[29] A.G. Vituškin, Theory of Transmission and Processing of Information (Translated from the Russian). Pergamon, New York, 1961. | MR 132342 | Zbl 0122.12001