Properties of the class of measure separable compact spaces

• Autorzy: Mirna Džamonja , Kenneth Kunen
• Języki publikacji: EN

Abstrakty

EN

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure is equivalent to the existence of a real-valued measurable cardinal ≤${\ninegot c}$. We show that not being in MS is preserved by all forcing extensions which do not collapse $ω_1$, while being in MS can be destroyed even by a ccc forcing.

Kategorie tematyczne

• 54D30: Compactness
• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
• 03E99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 3
• Strony: 261-277

Daty

wydano

1995

otrzymano

1994-08-29

Twórcy

autor

Mirna Džamonja

• Institute of Mathematics, Hebrew University of Jerusalem, 91904 Givat Ram, Israel

autor

Kenneth Kunen

• Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, U.S.A.

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