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Note on a plane measure problem

Published online by Cambridge University Press:  26 February 2010

H. T. Croft
H. T. Croft
Affiliation:
St. John's College, Cambridge.
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Extract

In this note we consider a problem which is suggested by a paper of W. Feller. A plane set A lies in a circle C of centre O and radius 1, and is such that the linear measure of the intersection of A with any straight line does not exceed 21, where 0 < l < 1. To find the upper bound of the plane measure of A. Both linear measure and plane measure are taken in the sense of Lebesgue, and they will be denoted by m and m2 respectively.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 2 , December 1958 , pp. 125 - 127
Copyright
Copyright © University College London 1958

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References

page 125 note * Duke Math. J., 9 (1942), 885–892.CrossRefGoogle Scholar

page 127 note * Journal London Math. Soc, 33 (1958), 82–84.Google Scholar