Nonseparable Radon measures and small compact spaces
نویسنده
چکیده
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 being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ ω2 this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of ω1 null sets in 21 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 = ω1. We also give alternative proofs of two related results due to Kunen and van Mill [18].
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