Topological spaces whose Baire measure admits a regular Borel extension

Authors:
Haruto Ohta and Ken-ichi Tamano

Journal:
Trans. Amer. Math. Soc. **317** (1990), 393-415

MSC:
Primary 28C15; Secondary 54C50, 54G20

DOI:
https://doi.org/10.1090/S0002-9947-1990-0946425-5

MathSciNet review:
946425

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Abstract: A completely regular, Hausdorff space is called a Măík space if every Baire measure on admits an extension to a regular Borel measure. We answer the questions about Măík spaces asked by Wheeler [29] and study their topological properties. In particular, we give examples of the following spaces: A locally compact, measure compact space which is not weakly Bairedominated; i.e., it has a sequence of regular closed sets such that whenever 's are Baire sets with ; a countably paracompact, non-Măík space; a locally compact, non-Măík space such that the absolute is a Măík space; and a locally compact, Măík space for which is not. It is also proved that Michael's product space is not weakly Baire-dominated.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-0946425-5

Keywords:
Măík space,
countably paracompact,
locally compact,
absolute,
Michael line,
Baire measure,
Borel measure,
regular Borel extension,
measure compact

Article copyright:
© Copyright 1990
American Mathematical Society