Mathematische Annalen

, Volume 115, Issue 1, pp 296–329

On the fundamental geometrical properties of linearly measurable plane sets of points (II)

  • A. S. Besicovitch
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References

  1. 2).
    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.Google Scholar
  2. 3).
    When talking of measurable sets we shall always mean sets of finite measure unless the opposite is stated.Google Scholar
  3. 4).
    Writing the product of sets we shall often omit the sign × for convenience of printing.Google Scholar
  4. 5).
    I, § 11, pp. 431–434.Google Scholar
  5. 6).
    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.Google Scholar
  6. 7).
    For a proof see R. Courant and D. Hilbert, Methoden der mathematischen Physik, Bd. I, Kap. II, § 2.Google Scholar
  7. 8).
    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.Google Scholar

Copyright information

© Springer-Verlag 1938

Authors and Affiliations

  • A. S. Besicovitch
    • 1
  1. 1.CambridgeEngland

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