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The 1996 Joint Spring Topology Conference and Southeast Dynamical Systems Conference
March 7-9, 1996
Ball State University
Muncie, IN, USA

Organizers
John Emert, Kerry Jones, Roger Nelson

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Additivity of quasi-measures
by
Tim LaBerge
Northern Illinois University
Coauthors: Dan Grubb

A quasi-measure on a compact Hausdorff space X is a finitely additive "measure" on A (the collection of subsets of X which are either open or closed) which is not required to be sub-additive. Thus, if \mu is a quasi-measure on X that is not a measure, then there are closed sets C1 and C2 such that \mu(C1) = 0 = \mu(C2), but \mu(C1 \cup C2) is not 0.

We prove that if \mu is a quasi-measure on a compact X, then \mu is countably additive. I.e., if {An} is contained in A and \cup An is an element of A, then \mu( \cup An) = \sum\mu(An). As a consequence, we obtain a correspondence between the collection of 0-1 quasi-measures on X and a subset of the collection of maximal linked families of closed connected subsets of X.

Date received: January 22, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-05.