On the additivity theorem for n-dimensional asymptotic density

Allen Roy Freedman

Vol. 49 (1973), No. 2, 357–363

DOI: 10.2140/pjm.1973.49.357

Abstract

“Additivity theorems” are approximations to countable additivity for set functions. A special case of the additivity theorem for natural density in n-dimensions is proved. To accomplish this a slightly different n-dimensional asymptotic density is defined for which the additivity theorem holds in general.

Mathematical Subject Classification

Primary: 10J99

Secondary: 10L10

Milestones

Received: 29 July 1972

Published: 1 December 1973