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On the right lower circular density of two-dimensional Jordan curves in the plane

Published online by Cambridge University Press:  24 October 2008

D. G. Larman
D. G. Larman
Affiliation:
University College London
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Extract

We use J(a, b) to denote a Jordan curve of positive two-dimensional measure in the plane, with end-points a and b. If υ is a point of J(a, b), we define the right lower arc density at υ by

where J( υ, υ′) is the largest arc, whose left-end point is υ, which is contained in the disc c(υ, r).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 67 - 70
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Besicovitch, A. S.Arcs and chords. Proc. London Math. Soc. (3) 14A (1965), 28–37.Google Scholar
(2)Besicovitch, A. S.Arcs and chords (11). J. London Math. Soc. 42 (1967), 86–92.Google Scholar