# Nonseparable Radon measures and small compact spaces

Fundamenta Mathematicae (1997)

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

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topPlebanek, 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 -

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