Vol. 27, No. 1, 1968

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On supports of regular Borel measures

Delma Joseph Hebert, Jr. and Howard E. Lacey

Vol. 27 (1968), No. 1, 101–118

The existence of a regular Borel measure whose support is a given compact Hausdorff space X imposes definite structures on X, C(X), and C(X). In this paper a necessary and sufficient condition is given to insure that X is the support of a regular Borel measure. This involves the intersection number of a collection of open sets in X. Measures which vanish on a sigma ideal of a sigma field of subsets of X which contains a basis for the topology of X are also considered. In particular, for a certain class of compact Hausdorff spacs X, necessary and sufficient conditions are given to insure the existence of a nonatomic regular Borel measure whose support is X. The final section of the paper is devoted to a study of normal measures; i.e., measures which vanish on meager Borel sets. Normal measures on X are shown to be related to normal measures on the projective resolution of X.

Mathematical Subject Classification
Primary: 28.13
Received: 19 July 1967
Published: 1 October 1968
Delma Joseph Hebert, Jr.
Howard E. Lacey