Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-29T04:23:25.023Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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