# Properties of the class of measure separable compact spaces

Fundamenta Mathematicae (1995)

- Volume: 147, Issue: 3, page 261-277
- ISSN: 0016-2736

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topDžamonja, Mirna, and Kunen, Kenneth. "Properties of the class of measure separable compact spaces." Fundamenta Mathematicae 147.3 (1995): 261-277. <http://eudml.org/doc/212088>.

@article{Džamonja1995,

abstract = {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 ≤$\{c\}$. 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.},

author = {Džamonja, Mirna, Kunen, Kenneth},

journal = {Fundamenta Mathematicae},

language = {eng},

number = {3},

pages = {261-277},

title = {Properties of the class of measure separable compact spaces},

url = {http://eudml.org/doc/212088},

volume = {147},

year = {1995},

}

TY - JOUR

AU - Džamonja, Mirna

AU - Kunen, Kenneth

TI - Properties of the class of measure separable compact spaces

JO - Fundamenta Mathematicae

PY - 1995

VL - 147

IS - 3

SP - 261

EP - 277

AB - 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 ≤${c}$. 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.

LA - eng

UR - http://eudml.org/doc/212088

ER -

## References

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