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Borel extensions of Baire measures in ZFC

100%

Kojman M., Michalewski H.

Fundamenta Mathematicae

2011

tom 211

nr 3

197-223

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.

Functions Equivalent to Borel Measurable Ones

81%

Komisarski A., Michalewski H., Milewski P.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

tom 58

nr 1

55-64

Let X and Y be two Polish spaces. Functions f,g: X → Y are called equivalent if there exists a bijection φ from X onto itself such that g∘φ = f. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Fundamenta Mathematicae

2 Michalewski H.

1 Kojman M.

1 Komisarski A.

1 Milewski P.

1 2011

1 2010

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Borel extensions of Baire measures in ZFC

Functions Equivalent to Borel Measurable Ones