Borel extensions of Baire measures in ZFC

Volume 211 / 2011

Menachem Kojman, Henryk Michalewski 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


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.


  • Menachem KojmanDepartment of Mathematics
    Ben-Gurion University of the Negev
    Beer Sheva, Israel
  • Henryk MichalewskiDepartment of Mathematics
    University of Warsaw
    02-097 Warszawa, Poland

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