We prove: 1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. 2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-1,
author = {Menachem Kojman and Henryk Michalewski},
title = {Borel extensions of Baire measures in ZFC},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {197-223},
zbl = {1222.28003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-1}
}
Menachem Kojman; Henryk Michalewski. Borel extensions of Baire measures in ZFC. Fundamenta Mathematicae, Tome 215 (2011) pp. 197-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-1/