Nonseparable Radon measures and small compact spaces

Plebanek, Grzegorz

Fundamenta Mathematicae, Tome 154 (1997), p. 25-40 / Harvested from The Polish Digital Mathematics Library

Résumé

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].

Détail

Publié le : 1997-01-01

Zbl 0905.28008

EUDML-ID : urn:eudml:doc:212213

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