Vol. 67, No. 2, 1976

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Regular lattice measures: mappings and spaces

George Bachman and Alan Sultan

Vol. 67 (1976), No. 2, 291–321

We prove in this paper a very general measure extension theorem which has as corollaries many recent, significant extension theorems in the literature. We apply these results to the question of when there is a well behaved map from the σ-smooth lattice regular measures on one set to the σsmooth lattice regular measures on a second set. After developing these general theorems we specialize consideration to two valued latitce regular measures and obtain in a new and consistent manner many important mapping and subspace theorems on the preservation of different types of repleteness including results of Dykes, Hager, Isiwata, Moran, Varadarajan, Gillman, Jerrison and others.

Mathematical Subject Classification
Primary: 28A55, 28A55
Received: 12 April 1976
Published: 1 December 1976
George Bachman
Alan Sultan