Borel extensions of Baire measures in ZF

Abstract

We prove: (1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel exten- sion. (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. © Instytut Matematyczny PAN, 2011.