Properties of the class of measure separable compact spaces

Mirna Džamonja; Kenneth Kunen

Fundamenta Mathematicae (1995)

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

Abstract

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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.

How to cite

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Džamonja, 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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  9. [9] R. Haydon, On dual L 1 -spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978), 142-152. Zbl0407.46018
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  11. [11] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287. 
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