Variations on vector measures

Gideon Schwarz

Vol. 23 (1967), No. 2, 373–375

DOI: 10.2140/pjm.1967.23.373

Abstract

Let, μ be a signed measure, and denote the total measure of its positive and negative parts by P and N. Since the total variation of such a measure is V = P + |N|, and the maximum of the absolute value of the measure is M = max(P,|N|), we have the inequality M ≦ V ≦ 2M. We consider the following question.

What should replace the constant 2 in this inequality when we pass to higher-dimensional vecstor-valued measures?

Mathematical Subject Classification

Primary: 28.50

Milestones

Received: 3 May 1967

Published: 1 November 1967