Borel extensions of Baire measures in ZFC
Volume 211 / 2011
Fundamenta Mathematicae 211 (2011), 197-223
MSC: Primary: 28A60, 03E04, 28C15, 03E35, 54A35;
Secondary 54G10, 28E15, 28A05, 03E75, 03E65, 03E55, 03E10, 54D15.
DOI: 10.4064/fm211-3-1
Abstract
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.
