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Hausdorff dimension of Banach spaces

Published online by Cambridge University Press:  20 January 2009

J. Arias De Reyna
J. Arias De Reyna
Affiliation:
Universidad de Sevilla, Facultad de Matemáticas, Apdo. 1160, 41080-Sevilla, Spain
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We show that if X is a Banach space of infinite dimension and μh is a Hausdorff measure, where h is continuous, then there exists a measurable set K ⊂ X such that 0<μh(K)< + ∞. We also characterize the normed spaces in which the unit ball can be covered by a sequence of balls whose radii rn < 1 converge to zero as n → ∞.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 217 - 229
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

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