ε-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms
Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 9 (1973) no. 2, pp. 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'institut Henri Poincar\'e. Section B. Calcul des probabilit\'es et statistiques},
     pages = {113--144},
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     volume = {9},
     number = {2},
     year = {1973},
     zbl = {0261.60011},
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     url = {http://archive.numdam.org/item/AIHPB_1973__9_2_113_0/}
}
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Gauglhofer, Margrit; Bharucha-Reid, A. T. $\varepsilon $-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms. Annales de l'institut Henri Poincaré. Section B. Calcul des probabilités et statistiques, Tome 9 (1973) no. 2, pp. 113-144. http://archive.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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

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

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

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

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

[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 | Zbl

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

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

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