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Parametric surfaces

II. Tangential properties

Published online by Cambridge University Press:  24 October 2008

E. R. Reifenberg
E. R. Reifenberg
Affiliation:
Trinity CollegeCambridge
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Extract

1. In this paper I investigate the tangential properties of parametric surfaces, leading to the main result that the Lebesgue area is the Hausdorff two-dimensional measure of the set of points of the surface where an approximate tangential plane exists.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 46 - 69
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Besicovitch, A. S.On the fundamental geometrical properties of linearly measurable plane sets of points. II. Math. Ann. 115 (1938), 296–329.CrossRefGoogle Scholar
(2)Besicovitch, A. S.A general form of the covering principle and the relative differentiation of additive functions. I. Proc. Camb. phil. Soc. 41 (1945), 103–10.CrossRefGoogle Scholar
(3)Besicovitch, A. S.On the definition and value of the area of a surface. Quart. J. Math. 16 (1945), 86–102.CrossRefGoogle Scholar
(4)Cesari, L.Una ugualianza fondamentale per l'area delle superficie. Mem. R. Accad. Ital. 14 (1944), 891–951. (See also p. 1379 of: Sui fondamenti geometrici dell' integrate classico per l'area delle superficie in forma parametrica. Mem. R. Accad. Ital. 13 (1943), 1323–481.)Google Scholar
(5)Reifenberg, E. R.Parametric surfaces. I. Area. Proc. Camb. phil. Soc. 47 (1951), 687–98.CrossRefGoogle Scholar