Vol. 90, No. 1, 1980

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ISSN: 0030-8730
[0, ]-valued, translation invariant measures on N and the Dedekind completion of R

Frank Arvey Wattenberg

Vol. 90 (1980), No. 1, 223–247
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
Authors
Frank Arvey Wattenberg