# ε-Entropy and moduli of smoothness in ${L}^{p}$-spaces

Studia Mathematica (1992)

- Volume: 102, Issue: 3, page 277-302
- ISSN: 0039-3223

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topKamont, A.. "ε-Entropy and moduli of smoothness in $L^{p}$-spaces." Studia Mathematica 102.3 (1992): 277-302. <http://eudml.org/doc/215929>.

@article{Kamont1992,

abstract = {The asymptotic behaviour of ε-entropy of classes of Lipschitz functions in $L^p(^d)$ is obtained. Moreover, the asymptotics of ε-entropy of classes of Lipschitz functions in $L^p(ℝ^d)$ whose tail function decreases as $O(λ^\{-γ\})$ is obtained. In case p = 1 the relation between the ε-entropy of a given class of probability densities on $ℝ^d$ and the minimax risk for that class is discussed.},

author = {Kamont, A.},

journal = {Studia Mathematica},

language = {eng},

number = {3},

pages = {277-302},

title = {ε-Entropy and moduli of smoothness in $L^\{p\}$-spaces},

url = {http://eudml.org/doc/215929},

volume = {102},

year = {1992},

}

TY - JOUR

AU - Kamont, A.

TI - ε-Entropy and moduli of smoothness in $L^{p}$-spaces

JO - Studia Mathematica

PY - 1992

VL - 102

IS - 3

SP - 277

EP - 302

AB - The asymptotic behaviour of ε-entropy of classes of Lipschitz functions in $L^p(^d)$ is obtained. Moreover, the asymptotics of ε-entropy of classes of Lipschitz functions in $L^p(ℝ^d)$ whose tail function decreases as $O(λ^{-γ})$ is obtained. In case p = 1 the relation between the ε-entropy of a given class of probability densities on $ℝ^d$ and the minimax risk for that class is discussed.

LA - eng

UR - http://eudml.org/doc/215929

ER -

## References

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- [7] P. Groeneboom, Some current developments in density estimation, in: Mathematics and Computer Science, Proceedings of the CWI symposium, November 1983, J. W. de Bakker, M. Hazewinkel and J. K. Lenstra (eds.), North-Holland, 1986, 163-192.
- [8] A. N. Kolmogorov and V. M. Tikhomirov, ε-Entropy and ε-capacity of sets in function spaces, Uspekhi Mat. Nauk 14 (2) (1959), 3-86 (in Russian); English transl.: Amer. Math. Soc. Transl. (2) 17 (1961), 277-364.
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