∈-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms

Margrit Gauglhofer; A. T. Bharucha-Reid

Annales de l'I.H.P. Probabilités et statistiques (1973)

  • Volume: 9, Issue: 2, page 113-144
  • ISSN: 0246-0203

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Gauglhofer, Margrit, and Bharucha-Reid, A. T.. "∈-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms." Annales de l'I.H.P. Probabilités et statistiques 9.2 (1973): 113-144. <http://eudml.org/doc/76973>.

@article{Gauglhofer1973,
author = {Gauglhofer, Margrit, Bharucha-Reid, A. T.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {2},
pages = {113-144},
publisher = {Gauthier-Villars},
title = {∈-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms},
url = {http://eudml.org/doc/76973},
volume = {9},
year = {1973},
}

TY - JOUR
AU - Gauglhofer, Margrit
AU - Bharucha-Reid, A. T.
TI - ∈-entropy of sets of probability distribution functions and their Fourier-Stieltjes transforms
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1973
PB - Gauthier-Villars
VL - 9
IS - 2
SP - 113
EP - 144
LA - eng
UR - http://eudml.org/doc/76973
ER -

References

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  1. [1] R. Adler, A. Konheim and M. Mcandrew, Topological entropy. Trans. Amer. Math. Soc., t. 11, 1965, p. 309-319. Zbl0127.13102MR175106
  2. [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. Zbl0244.46010MR410878
  3. [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. Zbl0248.60035MR348808
  4. [4] K.L. Chung, A Course in Probability Theory, Harcourt, Brace and World, New York, 1968. Zbl0159.45701MR229268
  5. [5] E.I. Dinaburg, The relation between topological entropy and metric entropy (Russian). Dokl. Acad. Nauk SSSR, t. 190, 1970, p. 19-22. Zbl0196.26401MR255765
  6. [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. Zbl0188.20502MR220340
  7. [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. Zbl0231.60029MR410879
  8. [8] R.M. Dudley, Small operators between Banach and Hilbert spaces. Studia Math., t. 38, 1970, p. 35-41. Zbl0205.43101MR275193
  9. [9] J. Dugundji, Topology. Allyn and Bacon, Boston, 1965. Zbl0144.21501MR478089
  10. [10] V.D. Erohin, Asymptotic theory of the ∈-entropy of analytic functions (Russian). Dokl. Akad. Nauk SSSR, t. 120, 1958, p. 949-952. Zbl0098.08701MR102744
  11. [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. Zbl0056.36001MR62975
  12. [12] L.W. Goodwyn, Topological entropy bounds measure-theoretic entropy. Proc. Amer. Math. Soc., t. 23, 1969, p. 679-688. Zbl0186.09804MR247030
  13. [13] A.I. Khinchin, Mathematical Foundations of Information Theory (Translated from the Russian), Dover, New York, 1957. Zbl0088.10404MR92709
  14. [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. Zbl0128.27803MR80129
  15. [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. Zbl0133.06703MR124720
  16. [16] M. Loève, Probability Theory, Third Ed., Van Nostrand, Princeton, N. J., 1963. Zbl0108.14202MR203748
  17. [17] G.G. Lorentz, Approximation of Functions. Holt, Rinehart and Winston, New York, 1966. Zbl0153.38901MR213785
  18. [18] G.G. Lorentz, Metric entropy and approximation. Bull. Amer. Math. Soc., t. 72, 1966, p. 903-937. Zbl0158.13603MR203320
  19. [19] E. Lukacs, Characteristic Functions, Griffin, London, 1960. Zbl0087.33605MR124075
  20. [20] E.C. Posner and E.R. Rodemich, Epsilon entropy and data compression. Ann. Math. Statist., t. 42, 1971, p. 2079-2125. Zbl0232.94007MR297458
  21. [21] R.T. Prosser, The ∈-entropy and ∈-capacity of certain time-varying channels. J. Math. Anal. Appl., t. 16, 1966, p. 553-573. Zbl0161.38702MR205750
  22. [22] R.T. Prosser, On the analysis and synthesis of certain abstract systems. Bull. Amer. Math. Soc., t. 77, 1971, p. 444-448. Zbl0213.49602MR274094
  23. [23] A. Rényi, Probability Theory. North-Holland, Amsterdam, 1970. Zbl0206.18002MR315747
  24. [24] J. Riordan, Introduction to Combinatorial Analysis. Wiley, New York, 1958. Zbl0078.00805MR96594
  25. [25] J. Riordan, Combinatorial Identities. Wiley, New York, 1968. Zbl0194.00502MR231725
  26. [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. Zbl0196.21101MR279872
  27. [27] V.N. Sudakov, Gaussian measures, Cauchy measures and ∈-entropy (Russian). Dokl. Akad. Nauk SSSR, t. 185, 1969, p. 51-53. Zbl0224.60018MR247034
  28. [28] A.G. Vituškin, On Hilbert's thirteenth problem (Russian). Dokl. Akad. Nauk SSSR, t. 95, 1954, p. 701-704. MR62212
  29. [29] A.G. Vituškin, Theory of Transmission and Processing of Information (Translated from the Russian). Pergamon, New York, 1961. Zbl0122.12001MR132342

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