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On families of domains

Published online by Cambridge University Press:  24 October 2008

A. S. Besicovitch
A. S. Besicovitch
Affiliation:
Trinity CollegeCambridge
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Extract

The boundary of a simply-connected plane domain in the simplest case is a Jordan curve, but in the general case it is of a very complicated nature. An interesting problem arises about the nature of the boundary, when we consider not a single domain but some extensive family of domains. The question is whether only exceptional domains of the family have a complicated boundary, the rest having simple ones.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 73 - 75
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCE

(1)Caratheodory, C.Die Begrenzung einfach zusammenhängender Gebiete. Math. Ann. 73 (1913), 366.Google Scholar