Vol. 82, No. 1, 1979

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Some relationships between measures

Roy Andrew Johnson

Vol. 82 (1979), No. 1, 117–132
Abstract

Suppose μ and ν are (nonnegative, countably additive) measures on the same sigma-ring. We say that ν is quasi-dominant with respect to μ if each measurable set contains a subset with the same ν-measure, where μ is absolutely continuous with respect to ν on that subset. In particular, ν is quasi-dominant with respect to μ if μ is sigma-finite. We say that ν is strongly recessive with respect to μ if the zero measure is the only measure that is quasi-dominant with respect to μ and less than or equal to ν. Properties of these relationships are investigated, and applications are given to purely atomic measures, to the Radon-Nikodým theorem and to a decomposition of product measures.

Mathematical Subject Classification 2000
Primary: 28A12
Milestones
Received: 12 November 1977
Published: 1 May 1979
Authors
Roy Andrew Johnson