Vol. 28, No. 1, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 297: 1
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
A theorem on sequential convergence of measures and some applications

John Bligh Conway

Vol. 28 (1969), No. 1, 53–60

If S is a locally compact Hausdorff space, let βS be its Stone-Cech compactification and let M(S) be the space of all finite complex valued regular Borel measures on S. In this paper we will prove that whenever S is paracompact and {μn} is a sequence in M(βS) which converges to zero in the weak star topology, then lim Sf dμn = 0 for every continuous function f, and {μn} satisfies a certain uniformity condition on S. This generalizes a result of R. S. Phillips on weak star sequential convergence in the dual of l. Moreover, by using our theorem we can obtain many previously known results whose proofs, though all similar, were apparently independent.

Mathematical Subject Classification
Primary: 46.25
Secondary: 28.00
Received: 11 December 1967
Published: 1 January 1969
John Bligh Conway