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On the fundamental geometrical properties of linearly measurable plane sets of points (II)
 A. S. Besicovitch
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Get AccessI. A. S. Besicovitch, Paper under the same title, Math. Annalen98 (1927)
 II. A. S. Besicovitch and G. Walker, On the density of irregular linearly measurable sets of points. Proc. of London Math. Soc. (L. M. S.)32 (1931), pp. 142–153. III. J. Gillis, On linearly measurable plane sets of points of upper density 1/2. Fund. Math.22, pp. 57–70. IV. J. Gillis, Note on the projection of irregular linearly measurable plane sets of points. Fund. Math.26, pp. 229–233. V. J. Gillis, A Theorem on irregular linearly measurable sets of points. Journal of L. M. S. 10, pp. 234–240. VI. G. W. Morgan, The density directions of irregular linearly measurable plane sets. Proc. of L. M. S.38 (1935), pp. 481–494. We shall refer the cited papers by the Roman figures standing in front of them.
 When talking of measurable sets we shall always mean sets of finite measure unless the opposite is stated.
 Writing the product of sets we shall often omit the sign × for convenience of printing.
 I, § 11, pp. 431–434.
 Δ (A, B) denotes the distance between the setsA andB, so that Δ (a _{0},a) is the distance between the pointsa _{0} anda, Δ (ψ,a) is the distance from the curve ψ to the pointa, and so on. — u. bd = upper bound.
 For a proof see R. Courant and D. Hilbert, Methoden der mathematischen Physik, Bd. I, Kap. II, § 2.
 We denote byE _{1}E _{2} the set of points ofE _{1} which do not belong toE _{2};E _{2} may or may not be entirely contained inE _{1}.
 Title
 On the fundamental geometrical properties of linearly measurable plane sets of points (II)
 Journal

Mathematische Annalen
Volume 115, Issue 1 , pp 296329
 Cover Date
 19381201
 DOI
 10.1007/BF01448943
 Print ISSN
 00255831
 Online ISSN
 14321807
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Authors

 A. S. Besicovitch ^{(1)}
 Author Affiliations

 1. Cambridge, England