Vol. 39, No. 2, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Measures on semilattices

Solomon Leader

Vol. 39 (1971), No. 2, 407–423

New definitions are given for positivity and bounded variation of functions on a semilattice S so that such functions extend to measures (respectively, signed measures) on the σ-algebra generated by some representation of S as a semilattice of sets under intersection. All such representations lie in a Stone space determined by S. Functions on a subsemilattice S of a distributive lattice L which extend to isotone valuations on L are characterized in terms of a partial ordering of finite sequences in S. Functions on a regulated semilattice which correspond to regular Borel measures on the associated locally compact space are characterized in terms of inclusion-exclusion sums.

Mathematical Subject Classification 2000
Primary: 28A60
Received: 4 November 1970
Published: 1 November 1971
Solomon Leader