On the fundamental geometrical properties of linearly measurable plane sets of points. II. (English) Zbl 0018.11302
Keywords:
Set theory, real functionsReferences:
| [1] | 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. · Zbl 0001.32803 |
| [2] | When talking of measurable sets we shall always mean sets of finite measure unless the opposite is stated. |
| [3] | Writing the product of sets we shall often omit the sign {\(\times\)} for convenience of printing. |
| [4] | I, § 11, pp. 431-434. |
| [5] | ? (A, B) denotes the distance between the setsA andB, so that ? (a 0,a) is the distance between the pointsa 0 anda, ? (?,a) is the distance from the curve ? to the pointa, and so on. ? u. bd = upper bound. |
| [6] | For a proof see R. Courant and D. Hilbert, Methoden der mathematischen Physik, Bd. I, Kap. II, § 2. · Zbl 0156.23201 |
| [7] | 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. |
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