# Measures on compact HS spaces

Fundamenta Mathematicae (1993)

- Volume: 143, Issue: 1, page 41-54
- ISSN: 0016-2736

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topDžamonja, Mirna, and Kunen, Kenneth. "Measures on compact HS spaces." Fundamenta Mathematicae 143.1 (1993): 41-54. <http://eudml.org/doc/211991>.

@article{Džamonja1993,

abstract = {We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of $2^\{ω_1\}$. The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a $G_δ$. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.},

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

journal = {Fundamenta Mathematicae},

keywords = {HS spaces; Radon probability measure; compact space},

language = {eng},

number = {1},

pages = {41-54},

title = {Measures on compact HS spaces},

url = {http://eudml.org/doc/211991},

volume = {143},

year = {1993},

}

TY - JOUR

AU - Džamonja, Mirna

AU - Kunen, Kenneth

TI - Measures on compact HS spaces

JO - Fundamenta Mathematicae

PY - 1993

VL - 143

IS - 1

SP - 41

EP - 54

AB - We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of $2^{ω_1}$. The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a $G_δ$. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.

LA - eng

KW - HS spaces; Radon probability measure; compact space

UR - http://eudml.org/doc/211991

ER -

## References

top- [1] V. V. Fedorchuk, On the cardinality of hereditarily separable compact spaces, Dokl. Akad. Nauk SSSR 222 (1975), 302-305 (in Russian). Zbl0331.54029
- [2] D. Fremlin, Consequences of Martin's Axiom, Cambridge University Press, 1984. Zbl0551.03033
- [3] A. Hajnal and I. Juhász, On first countable non-Lindelöf S-spaces, in: Colloq. Math. Soc. János Bolyai 10, North-Holland, 1975, 837-852.
- [4] R. Haydon, On dual ${L}^{1}$-spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978), 142-152. Zbl0407.46018
- [5] I. Juhász, K. Kunen and M. E. Rudin, Two more hereditarily separable non-Lindelöf spaces, Canad. J. Math. 28 (1976), 998-1005. Zbl0336.54040
- [6] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287.
- [7] D. Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108-111. Zbl0063.03723
- [8] J. Roitman, Basic S and L, in: Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, 1984, 295-326.

## Citations in EuDML Documents

top- Kenneth Kunen, Jan van Mill, Measures on Corson compact spaces
- Mirna Džamonja, Kenneth Kunen, Properties of the class of measure separable compact spaces
- David Fremlin, On compact spaces carrying Radon measures of uncountable Maharam type
- Grzegorz Plebanek, Nonseparable Radon measures and small compact spaces
- Grzegorz Plebanek, Approximating Radon measures on first-countable compact spaces

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