TY - JOUR
AU - Walker, G.
AB - 142 A. S. BESICOVITCH and G. WALKER [Dec. 12, ON TH E DENSITY OF IRREGULAR LINEARLY MEASURABLE SETS OF POINTS By A. S. BESICOVITCH and G. WALKER. [Received 15 November, 1929.—Read 12 December, 1929.J 1. Linearly measurable plane sets of points have been divided into two classest, the first consisting of regular and the second of irregular sets. The classification has been made in terms of density. Regular sets are those which possess the property that, at almost all points, the density exists and is equal to unity; and irregular sets are those for which, either the density does not exist, or, if it does, then it differs from unity. A general linearly measurable set can be divided into two subsets, one of which is regular and the other irregular. Regular sets form a natural generalization of rectifiable curves, since the fundamental geometrical properties of regular sets and rectifiable curves are the same. But irregular sets are completely dissimilar to these, and there is no gradual change of regular sets into irregular ones. It is very probable that the set of points of a general linearly measurable set, at which the density exists and differs from one, is of 
TI - On the Density of Irregular Linearly Measurable sets of Points
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s2-32.1.142
DA - 1931-01-01
UR - https://www.deepdyve.com/lp/wiley/on-the-density-of-irregular-linearly-measurable-sets-of-points-5geteECrTg
SP - 142
EP - 153
VL - s2-32
IS - 1
DP - DeepDyve
ER -