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Non σ-finite closed subsets of analytic sets

Published online by Cambridge University Press:  24 October 2008

Roy O. Davies
Roy O. Davies
Affiliation:
University CollegeLeicester
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Extract

A set is said to be σ-finite (with respect to Λs-measure) if it can be expressed as a countable sum of sets of finite Λs-measure. I have proved(1) that every non σ-finite analytic set in a Euclidean space contains a closed set of infinite measure, and Prof. Besicovitch asked me whether the closed subset could itself be chosen to be non σ-finite. In this paper an affirmative answer is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 2 , April 1956 , pp. 174 - 177
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Davies, R. O.Subsets of finite measure in analytic sets. Indag. math. 14 (1952), 488–9.CrossRefGoogle Scholar
(2)Davies, R. O.A property of Hausdorff measure. Proc. Camb. phil. Soc. 52 (1956), 30.CrossRefGoogle Scholar
(3)Saks, S.Theory of the integral (Warsaw, 1937).Google Scholar
(4)Siekpińskl, W.Une démonstration du théorème sur la structure des ensembles de points. Fundam. Math. 1 (1920), 1–6.Google Scholar
(5)Souslin, M.Sur une définition des ensembles mesurables (B) sans nombres transfinis. C.R. Acad. Sci., Paris, 164 (1917), 88–91.Google Scholar