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A note on linear derivates of measurable functions

Published online by Cambridge University Press:  24 October 2008

Roy O. Davies
Roy O. Davies
Affiliation:
University College Leicester
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Extract

By the measure of a set of directions in the plane we mean the linear measure of the set of points P on a unit circle for which the direction from the centre to P belongs to the set.

The ray issuing from a point P in direction θ will be denoted by P(θ).

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 153 - 155
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1) Neubauer, M.Über die partiellen Derivierten unstetiger Funktionen. Mh. Math. Phys. 38 (1931), 139–46.CrossRefGoogle Scholar
(2) Ward, A. J.The linear derivates and approximate linear derivates of a function of two variables. Proc. Lond. math. Soc. (2), 42 (1937), 266–73.CrossRefGoogle Scholar