This is a preview of subscription content, log in via an institution to check access.
Literatur
S. Saks, Théorie de l'intégrale, p. 169–175.
Long ago I thought that this theorem was true and I suggested to Mr Gillis that he should investigate from this side sets of upper density 1/2. By an ingenious method Gillis arrived at some partial results concerning this class of sets. He has also studied sets of directions from which an irregular set can be projected into a set of positive measure and he has constructed a set for which the set of such directions has the power of continuum in any angle, however small. I have quoted his papers in my paper II.
Author information
Authors and Affiliations
Additional information
Paper (II) under the same title has been published in Math. Annalen115 (1938). The literature to the question is given there.
Rights and permissions
About this article
Cite this article
Besicovitch, A.S. On the fundamental geometrical properties of linearly measurable plane sets of points (III). Math. Ann. 116, 349–357 (1939). https://doi.org/10.1007/BF01597361
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01597361