Skip to main content
SpringerLink
Log in

Entropy of the space of twice smooth curves in the Hausdorff metric

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Bound from above and below for the entropy of the space of twice smooth curves on a plane in the Hausdorff metric are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. N. Kolmogorov, “Bounds on the minimal number of elements of ɛ-nets in various functions spaces and their application to the problem of representing functions of several variables by superpositions of functions of a smaller number of variables,” Usp. Mat. Nauk,10, No. 1, 192–193 (1955).

    Google Scholar 

  2. A. N. Kolmogorov, “Asymptotic characteristics of certain completely bounded metric spaces,” Dokl. Akad. Nauk SSSR,108, 585–589 (1956).

    Google Scholar 

  3. A. G. Vitushkin, “On the thirteenth Hilbert problem,” Dokl. Akad. Nauk SSSR,95, No. 4, 701–704 (1955).

    Google Scholar 

  4. A. N. Kolmogorov and V. M. Tikhomirov, “ɛ-Entropy and ɛ-capacity of sets in functional spaces,” Usp. Mat. Nauk,14, No. 2, 3–86 (1959).

    Google Scholar 

  5. A. G. Vitushkin, “An absolute entropy of metric spaces,” Dokl. Akad. Nauk SSSR,117, No. 2, 745–748 (1957).

    Google Scholar 

  6. V. D. Erokhin, “On asymptotics of the ɛ-entropy of analytic functions,” Dokl. Akad. Nauk SSSR,120, No. 5, 949–952 (1958).

    Google Scholar 

  7. V. M. Tikhomirov, “On the ɛ-entropy of certain classes of analytic functions,” Dokl. Akad. Nauk SSSR,117, No. 2, 191–194 (1957).

    Google Scholar 

  8. M. Sh. Birman and M. Z. Solomyak, “Piecewisɛ-polynomial approximations of functions of W αp classes,” Mat. Sb.,73, No. 3, 331–355 (1967).

    Google Scholar 

  9. V. M. Tikhomirov, Some Problems of Approximation Theory [in Russian], Moscow Univ. Press (1976).

  10. Bl. Sendov and B. Penkov, “ɛ-Entropy and ɛ-capacity of the set of continuous functions,” Vestn. Mosk. Univ. Ser. Mat. Mekh., No. 3, 15–19 (1962).

    Google Scholar 

  11. Bl. Sendov and B. Penkov, “ɛ-Entropy and ɛ-capacity on the space of continuous functions,” Izv. Mat. Inst. Bulgarian Academy of Sciences, No. 6, 27–50 (1962) (in Bulgarian).

    Google Scholar 

  12. A. G. Vitushkin, Estimation of Complexity of the Tabulation Problem [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  13. A. A. Borovkov, A Course in Probability Theory [in Russian], Nauka, Moscow (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    N. V. Shcherbina

Authors
  1. N. V. Shcherbina
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 113–118, January, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shcherbina, N.V. Entropy of the space of twice smooth curves in the Hausdorff metric. Ukr Math J 42, 102–107 (1990). https://doi.org/10.1007/BF01066370

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01066370

Keywords

Search

Navigation