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Approximating sequences and Hausdorff measure

Published online by Cambridge University Press:  24 October 2008

R. J. Gardner
R. J. Gardner
Affiliation:
University College, London
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Approximating sequences have been extensively studied in many branches of mathematics, for example, in number theory (approximating real numbers by rationals) and in numerical analysis (approximations to functions by polynomials). In (1), A. Hyllengren introduced a type of approximating sequence ‘majorizing sequences’ which he used in solving a problem in complex analysis. In this note we study a very similar concept, which is general enough to be applicable to any separable metric space, and which turns out to have strong connexions with the theory of Hausdorff measures (as did Hyllengren's majorizing sequences).

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 161 - 172
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Hyllengren, A.On the lower order of f(z)e(z). Ark. Math. 6 (1966), 433–458.CrossRefGoogle Scholar
(2)Rogers, C. A. Hausdorffmeasures (Cambridge, 1970).Google Scholar
(3)Goodey, P. R.Generalized Hausdorff dimension. Mathematika 17 (1970), 324–327.CrossRefGoogle Scholar
(4)Körnre, T. W.Some covering theorems for infinite dimensional vector spaces. J. London Math. Soc. 2, 2 (1970), 643–646.CrossRefGoogle Scholar
(5)Gardner, R. J. and Hawkes, J. Majorizing sequences and approximation, to be submitted.Google Scholar