Nonseparable Radon measures and small compact spaces

Grzegorz Plebanek

Fundamenta Mathematicae (1997)

  • Volume: 153, Issue: 1, page 25-40
  • ISSN: 0016-2736

Abstract

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We investigate the problem if every compact space K carrying a Radon measure of Maharam type κ can be continuously mapped onto the Tikhonov cube [ 0 , 1 ] κ (κ being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ κ this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of ω 1 null sets in 2 ω 1 such that every perfect set meets one of them, we construct a compact space showing that the answer to the above problem is “no” for κ = ω. We also give alternative proofs of two related results due to Kunen and van Mill [18].

How to cite

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Plebanek, Grzegorz. "Nonseparable Radon measures and small compact spaces." Fundamenta Mathematicae 153.1 (1997): 25-40. <http://eudml.org/doc/212213>.

@article{Plebanek1997,
abstract = {We investigate the problem if every compact space K carrying a Radon measure of Maharam type κ can be continuously mapped onto the Tikhonov cube $[0, 1]^κ$ (κ being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ κ this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of $ω_1$ null sets in $2^\{ω1\}$ such that every perfect set meets one of them, we construct a compact space showing that the answer to the above problem is “no” for κ = ω. We also give alternative proofs of two related results due to Kunen and van Mill [18].},
author = {Plebanek, Grzegorz},
journal = {Fundamenta Mathematicae},
keywords = {Radon measure of Maharam type; measure algebras},
language = {eng},
number = {1},
pages = {25-40},
title = {Nonseparable Radon measures and small compact spaces},
url = {http://eudml.org/doc/212213},
volume = {153},
year = {1997},
}

TY - JOUR
AU - Plebanek, Grzegorz
TI - Nonseparable Radon measures and small compact spaces
JO - Fundamenta Mathematicae
PY - 1997
VL - 153
IS - 1
SP - 25
EP - 40
AB - We investigate the problem if every compact space K carrying a Radon measure of Maharam type κ can be continuously mapped onto the Tikhonov cube $[0, 1]^κ$ (κ being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ κ this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of $ω_1$ null sets in $2^{ω1}$ such that every perfect set meets one of them, we construct a compact space showing that the answer to the above problem is “no” for κ = ω. We also give alternative proofs of two related results due to Kunen and van Mill [18].
LA - eng
KW - Radon measure of Maharam type; measure algebras
UR - http://eudml.org/doc/212213
ER -

References

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