Borel extensions of Baire measures in ZFC

• Autorzy: Menachem Kojman , Henryk Michalewski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28A60: Measures on Boolean rings, measure algebras
• 03E55: Large cardinals
• 03E65: Other hypotheses and axioms
• 54A35: Consistency and independence results
• 03E75: Applications of set theory
• 03E35: Consistency and independence results
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets
• 03E04: Ordered sets and their cofinalities; pcf theory
• 28E15: Other connections with logic and set theory
• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
• 54G10: P -spaces
• 03E10: Ordinal and cardinal numbers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 3
• Strony: 197-223

Daty

wydano

2011

Twórcy

autor

Menachem Kojman

• Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

autor

Henryk Michalewski

• Department of Mathematics, University of Warsaw, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm211-3-1