Vol. 75, No. 1, 1978

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Coallocation between lattices with applications to measure extensions

William Josephson

Vol. 75 (1978), No. 1, 149–163
Abstract

It is well known that in a locally compact Hausdorff space every countably additive measure on Rσ(𝒦δ), the σ-ring generated by the compact Gδ sets, can be extended to a countably additive measure on σ(), the σ-algebra generated by the closed sets. In a locally compact Hausdorff space , the lattice of closed sets, countably coallocates (Definition 4.7) the lattice of compact Gδ sets. Our purpose is to show that coallocation and countable coallocation are properties basic to many extension theorems.

Mathematical Subject Classification 2000
Primary: 28A10
Milestones
Received: 11 February 1977
Published: 1 March 1978
Authors
William Josephson