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Thin sets in

Published online by Cambridge University Press:  20 January 2009

I. Tweddle
I. Tweddle
Affiliation:
University of Stirling, Stirling
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In (4) J. F. C. Kingman and A. P. Robertson introduced the idea of thin sets in certain ℒ1 spaces. Thin sets are extreme cases of sets which are not total, and so the problem naturally arises of partitioning a measure space relative to a given set of integrable functions in such a way that on each element of the partition, the set of functions is either thin or total in a sense which is made precise below. In the present note, such partitions are obtained in §2 for finite or totally σ-finite measure spaces. In §3 the basic ideas are reformulated in terms of Radon measures on locally compact spaces, leading to an extension of the results of §2 in this context.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 4 , December 1971 , pp. 311 - 316
Copyright
Copyright © Edinburgh Mathematical Society 1971

References

REFERENCES

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(4) Kingman, J. F. C. and Robertson, A. P., On a theorem of Lyapunov, J. London Math. Soc. 43 (1968), 347–351.CrossRefGoogle Scholar