Abstract

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 Both linear measure and plane measure are taken in the sense of Lebesgue, and they will be denoted by m and m 2 respectively.

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