[0, ∞]-valued, translation invariant measures on N and the Dedekind completion of ^∗R

Frank Arvey Wattenberg

Vol. 90 (1980), No. 1, 223–247

DOI: 10.2140/pjm.1980.90.223

Abstract

This paper investigates {0,∞}-valued, translation invariant measures on the set N of positive integers. The main tool in this investigation is Nonstandard Analysis and especially the completion, ^♯R, in the sense of Dedekind of the Nonstandard Reals, ^∗R. The algebraic and topological properties of ^♯R are developed and exploited to obtain a classification theorem for a particularly nice class of {0,∞}-valued, translation invariant measures on N.

Mathematical Subject Classification 2000

Primary: 26E35

Secondary: 03H05, 28A12

Milestones

Received: 25 April 1977

Revised: 10 July 1979

Published: 1 September 1980