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The Besicovitch dimension of Cartesian product sets

Published online by Cambridge University Press:  24 October 2008

H. G. Eggleston
H. G. Eggleston
Affiliation:
University CollegeSwansea
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Extract

A. S. Besicovitch has defined the dimension of a point-set X in n-dimensional Euclidean space in terms of its exterior Hausdorff measure as follows (2). Let (δ, X) be any enumerable class of sets whose point-set union contains X and whose members are each of diameter less than δ. Let (δ, X) denote the class of all (δ, X).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 3 , July 1950 , pp. 383 - 386
Copyright
Copyright © Cambridge Philosophical Society 1950

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References

REFERENCES

(1)Banach, S.Théorie dea opérations linéaires (Warsaw, 1932).Google Scholar
(2)Besicovitch, A. S.Linear sets of fractional dimensions. Math. Ann. 101 (1929), 161–93.CrossRefGoogle Scholar
(3)Besicovitch, A. S.Most concentrated and most rarefied sets. Acta Math. 62 (1934), 289–300.CrossRefGoogle Scholar
(4)Besicovitch, A. S and Moran, P. A. P.The measure of product and cylinder sets. J. London Math. Soc. 20 (1945), 110–20.Google Scholar
(5)Besicovitch, A. S. and Ursell, H. D.Sets of fractional dimension. V. J. London Math. Soc. 12 (1937), 18–25.CrossRefGoogle Scholar
(6)Choquet, Gustave. Ensembles singuliers et structure des ensembles mesurables pour les mesures de Hausdorff. Bull. Soc. Math. France, 74 (1946), 1–14.Google Scholar
(7)Loomis, H. L.The intrinsic measure theory of Riemannian and Euclidean metric spaces. Ann. Math. (2), 45 (1944), 367–74.CrossRefGoogle Scholar
(8)Mazur, S. Ref. in (1) and (9).Google Scholar
(9)Saks, S.Theory of the integral (Warsaw, 1937).Google Scholar