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Uspekhi Matematicheskikh Nauk, 1959, Volume 14, Issue 2(86), Pages 3–86 (Mi rm7289)  

This article is cited in 108 scientific papers (total in 108 papers)

εε-entropy and εε-capacity of sets in function spaces

A. N. Kolmogorov, V. M. Tikhomirov
Received: 15.12.1958
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. N. Kolmogorov, V. M. Tikhomirov, “εε-entropy and εε-capacity of sets in function spaces”, Russian Math. Surveys, 14:2 (1959)
Citation in format AMSBIB
\Bibitem{KolTik59}
\by A.~N.~Kolmogorov, V.~M.~Tikhomirov
\paper $\varepsilon$-entropy and $\varepsilon$-capacity of sets in function spaces
\jour Russian Math. Surveys
\yr 1959
\vol 14
\issue 2
\mathnet{http://mi.mathnet.ru/eng/rm7289}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=112032}
\zmath{https://zbmath.org/?q=an:0133.06703|0090.33503}
Linking options:
  • https://www.mathnet.ru/eng/rm7289
  • https://www.mathnet.ru/eng/rm/v14/i2/p3
  • This publication is cited in the following 108 articles:
    1. O. L. Vinogradov, “Average dimension of shift spaces and their subspaces”, Math. Notes, 116:5 (2024), 949–959  mathnet  crossref  crossref
    2. A. M. Vershik, M. A. Lifshits, “On mmmm-entropy of a Banach space with a Gaussian measure”, Theory Probab. Appl., 68:3 (2023), 431–439  mathnet  crossref  crossref
    3. Russian Math. Surveys, 78:4 (2023), 635–777  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. A. D. Smorodinov, T. V. Gavrilenko, V. A. Galkin, “Teoreticheskie osnovy iskusstvennykh neironnykh setei dlya resheniya zadachi approksimatsii i interpolyatsii”, Uspekhi kibernetiki, 4:4 (2023), 41–53  mathnet  crossref
    5. B. S. Darkhovsky, “Estimate of the Hölder Exponent Based on the ϵϵ-Complexity of Continuous Functions”, Math. Notes, 111:4 (2022), 628–631  mathnet  crossref  crossref
    6. D. B. Kats, “Integrirovanie po nespryamlyaemym krivym kak raspredelenie”, Materialy XVII Vserossiiskoi molodezhnoi shkoly-konferentsii «Lobachevskie chteniya-2018»,  23-28 noyabrya 2018 g., Kazan.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 176, VINITI RAN, M., 2020, 50–60  mathnet  crossref  mathscinet
    7. B. S. Darkhovsky, “On the complexity and dimension of continuous finite-dimensional maps”, Theory Probab. Appl., 65:3 (2020), 375–387  mathnet  crossref  crossref  isi  elib
    8. Sara Leulmi, Fatiha Messaci, “A class of local linear estimators with functional data”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 379–391  mathnet  crossref
    9. H. A. Petrosyan, “On the properties of the symbols of one class of hypoelliptic equations”, J. Appl. Industr. Math., 13:4 (2019), 698–705  mathnet  crossref  crossref
    10. M. M. Lange, “On comparative efficiency of classification schemes in an ensemble of data sources using average mutual information”, Inform. i ee primen., 13:4 (2019), 18–26  mathnet  crossref
    11. S. V. Buyalo, “Spectral geometries on a compact metric space”, St. Petersburg Math. J., 30:5 (2019), 821–839  mathnet  crossref  mathscinet  isi  elib
    12. G. K. Kamenev, “Method for constructing optimal dark coverings”, Comput. Math. Math. Phys., 58:7 (2018), 1040–1048  mathnet  crossref  crossref  isi  elib
    13. B. A. Kats, S. R. Mironova, A. Yu. Pogodina, “Jump boundary-value problem on a contour with elongate singularities”, Russian Math. (Iz. VUZ), 61:1 (2017), 10–13  mathnet  crossref  isi
    14. B. A. Kats, “Riemann boundary-value problem for holomorphic matrices on non-rectifiable curve”, Russian Math. (Iz. VUZ), 61:2 (2017), 17–27  mathnet  crossref  isi
    15. D. B. Katz, “Marcinkiewicz exponents and a boundary-value jump problem for Beltrami equation”, Russian Math. (Iz. VUZ), 61:6 (2017), 37–43  mathnet  crossref  isi
    16. A. A. Vasil'eva, “Entropy numbers of embedding operators of function spaces on sets with tree-like structure”, Izv. Math., 81:6 (2017), 1095–1142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. Bogachev V. Smolyanov O., “Topological Vector Spaces and Their Applications”, Topological Vector Spaces and Their Applications, Springer Monographs in Mathematics, Springer, 2017, 1–456  crossref  isi
    18. D. B. Kats, “New metric characteristics of nonrectifiable curves and their applications”, Siberian Math. J., 57:2 (2016), 285–291  mathnet  crossref  crossref  mathscinet  isi  elib
    19. V. N. Ushakov, P. D. Lebedev, “Algoritmy optimalnogo pokrytiya mnozhestv na ploskosti R2”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:2 (2016), 258–270  mathnet  crossref  mathscinet  elib
    20. G. K. Kamenev, “Multicriteria identification sets method”, Comput. Math. Math. Phys., 56:11 (2016), 1843–1858  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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